Question 1

Lactose intolerance affects about 10% of non-Hispanic white Americans, 50% of Hispanic Americans, and 70% of African, Asian, and Native Americans. Seventy-four percent of U.S. residents are non-Hispanic whites, 10% of them are Hispanic, and 11% are African, Asian, or Native American. If a person is selected from this group of people, what is the probability, to four decimal places, that the person will be lactose intolerant? ​
A) Pr(lactose intolerant) = 0.1240
B) Pr(lactose intolerant) = 0.2010
C) Pr(lactose intolerant) = 0.1270
D) Pr(lactose intolerant) = 0.1510
E) Pr(lactose intolerant) = 0.1310

Accepted Answer

The answer of Lactose intolerance affects about 10% of non-Hispanic...

Question 2

Assuming there are 365 different birthdays, find the probability that at least two of nine people chosen at random will have same birthdays. Round your answer to five decimal places. ​
A) 0.04895
B) 0.00538
C) 0.81075
D) 0.54731
E) 0.09462

Accepted Answer

The answer of Assuming there are 365 different birthdays, find...

Question 3

A bag contains 7 white balls and 3 red balls. Construct a probability tree to determine the probability that if 2 balls are drawn, with replacement, both balls are red R. ​
A) Pr(both R) = 
B) Pr(both R) = 
C) Pr(both R) = 
D) Pr(both R) = 
E) Pr(both R) =

Accepted Answer

The answer of A bag contains 7 white balls and...

Question 4

An urn contains 7 red, 3 white, and 6 black balls. One ball is drawn from the urn, it is replaced, and a second ball is drawn. Construct a probability tree to determine the probability that one ball is white W and one is red R. ​
A) Pr(one W ∩ one R) = 
B) Pr(one W ∩ one R) = 
C) Pr(one W ∩ one R) = 
D) Pr(one W ∩ one R) = 
E) Pr(one W ∩ one R) =

Accepted Answer

The probability tree for the given scenario would look like this:

R          W          B
           /     \     /     \     /    \
          R      W     B     R    W    B
         / \    /  \  / \   / \   / \  / \
        R  W  R   W B  R W   R  W  B R  W

The probability of selecting a white ball on the first draw is 3/16, and the probability of selecting a red ball on the second draw is also 7/16. The probability of selecting a red ball on the first draw is 7/16, and the probability of selecting a white ball on the second draw is 3/16.

To calculate the probability of getting one white ball and one red ball, we can add the probabilities of the two possible outcomes:

(3/16) * (7/16) + (7/16) * (3/16) = 42/256

Simplifying, we get:

42/256 = 21/128

Therefore, the correct choice is C.

Question 5

Three balls are drawn, without replacement, from a bag containing 8 red balls and 6 white balls. Construct a probability tree to determine the probability that the third ball drawn is red R. ​
A) Pr(third ball R) = 
B) Pr(third ball R) = 
C) Pr(third ball R) = 
D) Pr(third ball R) = 
E) Pr(third ball R) =

Accepted Answer

The answer of Three balls are drawn, without replacement, from...

Question 6

Assuming there are 365 different birthdays, find the probability that five people chosen at random will have different birthdays. Round your answer to five decimal places. ​
A) 0.97736
B) 0.84986
C) 0.87286
D) 0.48643
E) 0.97286

Accepted Answer

The probability that five people chosen at random will have different birthdays can be calculated using the multiplication rule for independent events. For the first person, any birthday is possible, so the probability is 365/365. For the second person, to have a different birthday, there are 364 choices out of 365. For the third person, there are 363 choices, and so on. Thus, the probability is (365/365) * (364/365) * (363/365) * (362/365) * (361/365) = 0.97286 when rounded to five decimal places.

Question 7

Three balls are drawn, without replacement, from a bag containing 9 red balls and 4 white balls. Construct a probability tree to determine the probability that three white W balls are drawn. ​
A) Pr(three W) = 
B) Pr(three W) = 
C) Pr(three W) = 
D) Pr(three W) = 
E) Pr(three W) =

Accepted Answer

The answer of Three balls are drawn, without replacement, from...

Question 8

A bag contains 5 white balls and 5 red balls. Construct a probability tree to determine the probability that if 2 balls are drawn, with replacement, the first ball is red R or the second is white W. ​
A) Pr(R first ∪ W second) = 
B) Pr(R first ∪ W second) = 1
C) Pr(R first ∪ W second) = 
D) Pr(R first ∪ W second) = 
E) Pr(R first ∪ W second) =

Accepted Answer

The answer of A bag contains 5 white balls and...

Question 9

A bag contains 5 coins, of which 4 are fair; the remaining coin has a head on both sides. If a coin is selected at random from the bag and tossed three times, construct a probability tree to determine the probability that heads will occur at least twice. ​
A) Pr(at least two heads) = 
B) Pr(at least two heads) = 
C) Pr(at least two heads) = 
D) Pr(at least two heads) = 
E) Pr(at least two heads) =

Accepted Answer

First, we need to determine the probability of selecting each coin from the bag:

- Probability of selecting a fair coin = 4/5 
- Probability of selecting the double-headed coin = 1/5

Using this information, we can construct the probability tree:

[Please refer to the image in the link below]

The branches represent the outcomes of each coin toss, and the probabilities are calculated by multiplying the probabilities of the previous event and the corresponding outcome.

To find the probability of getting at least two heads, we need to add up the probabilities of the following outcomes:

- HHH (three heads) 
- HHT (two heads, one tail) 
- HTH (two heads, one tail) 
- THH (two heads, one tail)

The probability of getting three heads when tossing a fair coin is (1/2)^3 = 1/8. The probability of getting two heads and one tail when tossing a fair coin is 3*(1/2)^3 = 3/8 (since there are three ways to arrange two heads and one tail). The probability of getting two heads when tossing the double-headed coin is 1.

Using these probabilities, we can calculate the overall probability of getting at least two heads:

- Probability of getting at least two heads = (4/5)*(3/8) + (4/5)*(1/8) + (1/5)*1 
- Probability of getting at least two heads = 3/10 + 1/5 + 1/5 
- Probability of getting at least two heads = 11/20

Therefore, the correct answer is C.

Question 10

An urn contains 8 red, 9 white, and 2 black balls. One ball is drawn from the urn, it is replaced, and a second ball is drawn. Construct a probability tree to determine the probability that at least one ball drawn is black B. ​
A) Pr(at least one B) = 
B) Pr(at least one B) = 
C) Pr(at least one B) = 
D) Pr(at least one B) = 
E) Pr(at least one B) =

Accepted Answer

The probability tree for the given problem is as follows:

R (8/19)      
       /   \       
      R     W
     / \   / \
    R   W R   W
   / \ / \/ \ / \
  R  W R W R W R W
 B B B B B B B B

The probability of getting at least one black ball can be calculated by finding the probability of getting one black ball and the probability of getting two black balls and then adding them.

Probability of getting one black ball = 2/19 (since there are 2 black balls out of 19 total balls)

Probability of getting two black balls = (2/19) x (2/19) = 4/361

Therefore, the probability of getting at least one black ball is:

2/19 + 4/361 = 0.117647

Rounding to three decimal places, we get 0.118.

The closest answer choice to 0.118 is D, with a value of 0.119. Therefore, the best choice is D.

Question 11

A bag contains 7 white balls and 8 red balls. Construct a probability tree to determine the probability that if 2 balls are drawn,with replacement, the first ball is red R and the second is white W. ​
A) Pr(R first ∩ W second) = 
B) Pr(R first ∩ W second) = 
C) Pr(R first ∩ W second) = 
D) Pr(R first ∩ W second) = 
E) Pr(R first ∩ W second) =

Accepted Answer

The probability tree for selecting two balls with replacement is as follows:

R                        W
         /       \                 /       \
        8/15    7/15             8/15     7/15
        /           \            /            \
       R           W          R            W

To find the probability of getting a red ball first and a white ball second, we multiply the probabilities along the branch for R followed by W:

P(R first ∩ W second) = (8/15) x (7/15) = 56/225

Thus, the best choice is D).

Question 12

A bag contains 9 white balls and 5 red balls. Three balls are drawn, without replacement, from the bag. Construct a probability tree to determine the probability that all three balls are white W. ​
A) Pr(three W) = 
B) Pr(three W) = 
C) Pr(three W) = 
D) Pr(three W) = 
E) Pr(three W) =

Accepted Answer

The answer of A bag contains 9 white balls and...

Question 13

Three balls are drawn, without replacement, from a bag containing 9 red balls and 7 white balls. Construct a probability tree to determine the probability that two white W balls and one red R ball are drawn in any order. ​
A) Pr(two W ∩ one R) = 
B) Pr(two W ∩ one R) = 
C) Pr(two W ∩ one R) = 
D) Pr(two W ∩ one R) = 
E) Pr(two W ∩ one R) =

Accepted Answer

The probability tree is as follows:

R (9/16)
         /   \
        W   W (7/15)(6/14)
       /     \
      W      W (7/15)(5/14)
     /         \
    W          W (6/15)(5/14)

The probability of getting two white balls and one red ball in any order is the sum of the probabilities of getting RWW, WRW, and WWR.

RWW has a probability of (9/16) x (7/15) x (6/14) = 21/160

WRW has a probability of (9/16) x (7/15) x (6/14) = 21/160

WWR has a probability of (7/16) x (6/15) x (9/14) = 21/160

Adding these probabilities together gives 63/160, which is choice (B).

Question 14

A bag contains 5 white balls and 5 red balls. Construct a probability tree to determine the probability that if 2 balls are drawn,with replacement, one ball is red R and one is white W. ​
A) Pr(one R ∩one W) = 
B) Pr(one R ∩one W) = 
C) Pr(one R ∩one W) = 
D) Pr(one R ∩one W) = 
E) Pr(one R ∩one W) =

Accepted Answer

The answer of A bag contains 5 white balls and...

Question 15

A bag contains 9 white balls W and 9 red balls R. Three balls are drawn, without replacement, from the bag. Construct a probability tree to determine the probability that at least one white W ball is drawn. ​
A) Pr(at least one W) = 
B) Pr(at least one W) = 
C) Pr(at least one W) = 
D) Pr(at least one W) = 
E) Pr(at least one W) =

Accepted Answer

The answer of A bag contains 9 white balls W...

Question 16

An urn contains 4 red, 7 white, and 9 black balls. One ball is drawn from the urn, it is replaced, and a second ball is drawn. Construct a probability tree to determine the probability that both balls are white W. ​
A) Pr(both W) = 
B) Pr(both W) = 
C) Pr(both W) = 
D) Pr(both W) = 
E) Pr(both W) =

Accepted Answer

The answer of An urn contains 4 red, 7 white,...

Question 17

Suppose that a marksman hits the bull's-eye 1 time in 40 shots. If the next 4 shots are independent, find the probability that all of the next 4 shots hit the bull's-eye. ​
A) Pr(four bull's-eyes) = 
B) Pr(four bull's-eyes) = 
C) Pr(four bull's-eyes) = 
D) Pr(four bull's-eyes) = 
E) Pr(four bull's-eyes) =

Accepted Answer

The answer of Suppose that a marksman hits the bull's-eye...

Question 18

A bag contains 7 white balls and 8 red balls. Three balls are drawn, without replacement, from the bag. Construct a probability tree to determine the probability that exactly one white W ball is drawn. ​
A) Pr(exactly one W) = 
B) Pr(exactly one W) = 
C) Pr(exactly one W) = 
D) Pr(exactly one W) = 
E) Pr(exactly one W) =

Accepted Answer

The answer of A bag contains 7 white balls and...

Question 19

An unprepared student must take a 7-question, multiple-choice test that has 5 possible answers per question. If the student can eliminate two of the possible answers on the first three questions, and if she guesses on every question, what is the probability that she will answer at least one question correctly? ​
A) Pr(at least 1 correct) = 
B) Pr(at least 1 correct) = 
C) Pr(at least 1 correct) = 
D) Pr(at least 1 correct) = 
E) Pr(at least 1 correct) =

Accepted Answer

The answer of An unprepared student must take a 7-question,...

Question 20

Each of urns I and II has 2 red balls, 4 white balls, and 4 green balls. Urn III has 2 red balls, 5 white balls, and 3 green balls. An urn is selected at random and a ball is drawn. If the ball is green G, find the probability that urn III was selected. ​
A) Pr(III | G) = 
B) Pr(III | G) = 
C) Pr(III | G) = 
D) Pr(III | G) = 
E) Pr(III | G) =

Accepted Answer

The answer of Each of urns I and II has...

Quiz 7: Introduction to Probability

Assuming there are 365 different birthdays, find the probability that at least two of nine people chosen at random will have same birthdays. Round your answer to five decimal places. ​

A bag contains 7 white balls and 3 red balls. Construct a probability tree to determine the probability that if 2 balls are drawn, with replacement, both balls are red R. ​

An urn contains 7 red, 3 white, and 6 black balls. One ball is drawn from the urn, it is replaced, and a second ball is drawn. Construct a probability tree to determine the probability that one ball is white W and one is red R. ​

Three balls are drawn, without replacement, from a bag containing 8 red balls and 6 white balls. Construct a probability tree to determine the probability that the third ball drawn is red R. ​

Assuming there are 365 different birthdays, find the probability that five people chosen at random will have different birthdays. Round your answer to five decimal places. ​

Three balls are drawn, without replacement, from a bag containing 9 red balls and 4 white balls. Construct a probability tree to determine the probability that three white W balls are drawn. ​

A bag contains 5 white balls and 5 red balls. Construct a probability tree to determine the probability that if 2 balls are drawn, with replacement, the first ball is red R or the second is white W. ​

A bag contains 5 coins, of which 4 are fair; the remaining coin has a head on both sides. If a coin is selected at random from the bag and tossed three times, construct a probability tree to determine the probability that heads will occur at least twice. ​

An urn contains 8 red, 9 white, and 2 black balls. One ball is drawn from the urn, it is replaced, and a second ball is drawn. Construct a probability tree to determine the probability that at least one ball drawn is black B. ​

A bag contains 7 white balls and 8 red balls. Construct a probability tree to determine the probability that if 2 balls are drawn,with replacement, the first ball is red R and the second is white W. ​

A bag contains 9 white balls and 5 red balls. Three balls are drawn, without replacement, from the bag. Construct a probability tree to determine the probability that all three balls are white W. ​

Three balls are drawn, without replacement, from a bag containing 9 red balls and 7 white balls. Construct a probability tree to determine the probability that two white W balls and one red R ball are drawn in any order. ​

A bag contains 5 white balls and 5 red balls. Construct a probability tree to determine the probability that if 2 balls are drawn,with replacement, one ball is red R and one is white W. ​

A bag contains 9 white balls W and 9 red balls R. Three balls are drawn, without replacement, from the bag. Construct a probability tree to determine the probability that at least one white W ball is drawn. ​

An urn contains 4 red, 7 white, and 9 black balls. One ball is drawn from the urn, it is replaced, and a second ball is drawn. Construct a probability tree to determine the probability that both balls are white W. ​

Suppose that a marksman hits the bull's-eye 1 time in 40 shots. If the next 4 shots are independent, find the probability that all of the next 4 shots hit the bull's-eye. ​

A bag contains 7 white balls and 8 red balls. Three balls are drawn, without replacement, from the bag. Construct a probability tree to determine the probability that exactly one white W ball is drawn. ​

Each of urns I and II has 2 red balls, 4 white balls, and 4 green balls. Urn III has 2 red balls, 5 white balls, and 3 green balls. An urn is selected at random and a ball is drawn. If the ball is green G, find the probability that urn III was selected. ​

Assuming there are 365 different birthdays, find the probability that at least two of nine people chosen at random will have same birthdays. Round your answer to five decimal places.

A bag contains 7 white balls and 3 red balls. Construct a probability tree to determine the probability that if 2 balls are drawn, with replacement, both balls are red R.

An urn contains 7 red, 3 white, and 6 black balls. One ball is drawn from the urn, it is replaced, and a second ball is drawn. Construct a probability tree to determine the probability that one ball is white W and one is red R.

Three balls are drawn, without replacement, from a bag containing 8 red balls and 6 white balls. Construct a probability tree to determine the probability that the third ball drawn is red R.

Assuming there are 365 different birthdays, find the probability that five people chosen at random will have different birthdays. Round your answer to five decimal places.

Three balls are drawn, without replacement, from a bag containing 9 red balls and 4 white balls. Construct a probability tree to determine the probability that three white W balls are drawn.

A bag contains 5 white balls and 5 red balls. Construct a probability tree to determine the probability that if 2 balls are drawn, with replacement, the first ball is red R or the second is white W.

A bag contains 5 coins, of which 4 are fair; the remaining coin has a head on both sides. If a coin is selected at random from the bag and tossed three times, construct a probability tree to determine the probability that heads will occur at least twice.

An urn contains 8 red, 9 white, and 2 black balls. One ball is drawn from the urn, it is replaced, and a second ball is drawn. Construct a probability tree to determine the probability that at least one ball drawn is black B.

A bag contains 7 white balls and 8 red balls. Construct a probability tree to determine the probability that if 2 balls are drawn,with replacement, the first ball is red R and the second is white W.

A bag contains 9 white balls and 5 red balls. Three balls are drawn, without replacement, from the bag. Construct a probability tree to determine the probability that all three balls are white W.

Three balls are drawn, without replacement, from a bag containing 9 red balls and 7 white balls. Construct a probability tree to determine the probability that two white W balls and one red R ball are drawn in any order.

A bag contains 5 white balls and 5 red balls. Construct a probability tree to determine the probability that if 2 balls are drawn,with replacement, one ball is red R and one is white W.

A bag contains 9 white balls W and 9 red balls R. Three balls are drawn, without replacement, from the bag. Construct a probability tree to determine the probability that at least one white W ball is drawn.

An urn contains 4 red, 7 white, and 9 black balls. One ball is drawn from the urn, it is replaced, and a second ball is drawn. Construct a probability tree to determine the probability that both balls are white W.

Suppose that a marksman hits the bull's-eye 1 time in 40 shots. If the next 4 shots are independent, find the probability that all of the next 4 shots hit the bull's-eye.

A bag contains 7 white balls and 8 red balls. Three balls are drawn, without replacement, from the bag. Construct a probability tree to determine the probability that exactly one white W ball is drawn.

Each of urns I and II has 2 red balls, 4 white balls, and 4 green balls. Urn III has 2 red balls, 5 white balls, and 3 green balls. An urn is selected at random and a ball is drawn. If the ball is green G, find the probability that urn III was selected.