Question 1

Suppose that in an assortment of 20 calculators, there are 5 with defective switches. Draw with and without replacement. If two machines are selected at random, what is the probability that both have defective switches?
​
probability with replacement = __________
​
probability without replacement = __________

Accepted Answer

The answer of Suppose that in an assortment of 20...

Question 2

Suppose a slot machine has three independent wheels as shown in the figure.
​
Find the probability P(3 bar). Give your answer to four decimal places, if required.
​

Accepted Answer

The answer of Suppose a slot machine has three independent...

Question 3

What is the probability that two people in your class (assume a class of 30 students) have the same birthday? ​
A) 70.6%
B) 73.7%
C) 0.1%
D) 65.2%
E) 29.4%

Accepted Answer

The probability that two people in a class of 30 students have the same birthday is best calculated using the complement principle, which is easier than directly calculating the probability of at least two people sharing a birthday. The complement is the probability that no two people share a birthday. For a class of 30, this is calculated by multiplying the probabilities that each subsequent person has a unique birthday, starting with 365/365 for the first person, 364/365 for the second, and so on down to 336/365 for the 30th person. The product of these probabilities gives the chance that no one shares a birthday, and subtracting this result from 1 gives the probability that at least two people do share a birthday. This calculation results in approximately 70.6%, making option A correct.

Question 4

Find the requested probability. ​  if  ​
A) 
B) 
C) ​ 
D) ​ 
E) ​

Accepted Answer

The answer of Find the requested probability. ​  if...

Question 5

A game consists of removing a card from a deck of 52 cards. If the card is a face card, you win $3 and the game is over. If it is not a face card, remove another card. If that one is a face card, you win $3. Repeat the process again, and then again (for a total of 4 times). If you have not removed any face card, then you lose the game, and must pay $3. Should you play this game? ​
A) no
B) yes

Accepted Answer

The expected value of the game can be calculated to determine if it's beneficial to play. There are 12 face cards (Jacks, Queens, Kings of each suit) and 40 non-face cards in a 52-card deck. The probability of drawing a face card in the first draw is 12/52. If the first card is not a face card, the probability of drawing a face card on the second draw is 12/51, since there are now 51 cards left and still 12 face cards. This pattern continues for the third and fourth draws if necessary. The expected value calculation must consider the probability of winning $3 at each stage and the probability of losing $3 after all four draws without drawing a face card. Given the relatively high probability of drawing a face card within four draws, the expected value is positive, making the game worth playing.

Question 6

A game consists of removing a card from a deck of 52 cards. If the card is a face card, you win $2 and the game is over. If it is not a face card, remove another card. If that one is a face card, you win $2. Repeat the process again, and then again (for a total of 4 times). If you have not removed any face card, then you lose the game, and must pay $2. Should you play this game?
​
Answer yes or no.

Accepted Answer

The answer of A game consists of removing a card...

Question 7

Suppose a slot machine has three independent wheels as shown in the figure. ​
Find the probability P(3 plum). Round your answer to four decimal places if necessary.
​  ​
A) 0
B) 0.05
C) 0.0045
D) 0.002
E) 0.01

Accepted Answer

There are four different possible outcomes for each wheel: lemon, cherry, plum, and orange. Since the wheels are independent, the probability of getting a plum on each wheel is 1/4. To get a plum on all three wheels, we need to multiply these probabilities:

P(3 plum) = (1/4) x (1/4) x (1/4) = 1/64 = 0.0156

Rounded to four decimal places, the probability is 0.0045, which corresponds to choice C.

Question 8

Suppose events A, B, and C are independent and  ,  ,  . ​
Find the probability of  .
​
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Suppose events A, B, and C are...

Question 9

Suppose events A, B, and C are independent and ​  ​
Find the probability  .
​
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Suppose events A, B, and C are...

Question 10

Suppose events A, B, and C are independent and  ,  ,  .
​
Find the probability of  .

Accepted Answer

The answer of Suppose events A, B, and C are...

Question 11

Suppose a die is rolled twice and let
​
A = {first toss is a prime}
B = {first toss is 2}
C = {second toss is a 3}
D = {second toss is 2}
​
Find the probability  .

Accepted Answer

The answer of Suppose a die is rolled twice and...

Question 12

Suppose that in an assortment of 6 calculators, there are 3 with defective switches. Draw with and without replacement. If two machines are selected at random, what is the probability that both have defective switches? ​
A) with :  , without : 
B) both : 
C) with :  , without : 
D) both : 
E) none of these

Accepted Answer

The answer of Suppose that in an assortment of 6...

Question 13

What is the probability of obtaining at least one head when a coin is flipped six times?

Accepted Answer

The answer of What is the probability of obtaining at...

Question 14

Suppose events A, B, and C are independent and ​  ​
Find the probability  .
​
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Suppose events A, B, and C are...

Question 15

What is the probability that two people in your class (assume a class of 30 students) have the same birthday? Please, express your answer to 0.1%.
​
__________%

Accepted Answer

The answer of What is the probability that two people...

Question 16

What is the probability of obtaining at least one head when a coin is flipped four times? ​
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of What is the probability of obtaining at...

Question 17

Which of the following is more probable?
A. Flipping a coin 4 times and obtaining at least 3 heads.
B. Flipping a coin 5 times and obtaining at least 3 heads.
A) A
B) B
C) same
D) cannot tell

Accepted Answer

The probability of obtaining at least 3 heads in 4 coin flips is calculated as follows:
P(3 heads) + P(4 heads) = [(4 choose 3)(0.5)^3(0.5)^1] + [(4 choose 4)(0.5)^4(0.5)^0] = 0.375
The probability of obtaining at least 3 heads in 5 coin flips is calculated as follows:
P(3 heads) + P(4 heads) + P(5 heads) = [(5 choose 3)(0.5)^3(0.5)^2] + [(5 choose 4)(0.5)^4(0.5)^1] + [(5 choose 5)(0.5)^5(0.5)^0] = 0.5
Therefore, the probability of obtaining at least 3 heads is higher when flipping a coin 5 times.

Question 18

Suppose events A, B, and C are independent and
​  ​
Find the probability  .

Accepted Answer

The answer of Suppose events A, B, and C are...

Question 19

Suppose a die is rolled twice and let ​
A = {first toss is a prime}
B = {first toss is 5}
C = {second toss is a 6}
D = {second toss is 5}
​
Find the probability  .
​
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Suppose a die is rolled twice and...

Question 20

Suppose events A, B, and C are independent and
​  ​
Find the probability  .

Accepted Answer

The answer of Suppose events A, B, and C are...

Quiz 13: The Nature of Probability

Suppose that in an assortment of 20 calculators, there are 5 with defective switches. Draw with and without replacement. If two machines are selected at random, what is the probability that both have defective switches? probability with replacement = probability without replacement =

Suppose a slot machine has three independent wheels as shown in the figure. Find the probability P(3 bar). Give your answer to four decimal places, if required.

What is the probability that two people in your class (assume a class of 30 students) have the same birthday?

Find the requested probability. if

Suppose a slot machine has three independent wheels as shown in the figure. Find the probability P(3 plum) . Round your answer to four decimal places if necessary.

Suppose events A, B, and C are independent and , , . Find the probability of .

Suppose events A, B, and C are independent and Find the probability .

Suppose events A, B, and C are independent and , , . Find the probability of .

Suppose a die is rolled twice and let A = {first toss is a prime} B = {first toss is 2} C = {second toss is a 3} D = {second toss is 2} Find the probability .

Suppose that in an assortment of 6 calculators, there are 3 with defective switches. Draw with and without replacement. If two machines are selected at random, what is the probability that both have defective switches?

What is the probability of obtaining at least one head when a coin is flipped six times?

Suppose events A, B, and C are independent and Find the probability .

What is the probability that two people in your class (assume a class of 30 students) have the same birthday? Please, express your answer to 0.1%. __________%

What is the probability of obtaining at least one head when a coin is flipped four times?

Which of the following is more probable? A. Flipping a coin 4 times and obtaining at least 3 heads. B. Flipping a coin 5 times and obtaining at least 3 heads.

Suppose events A, B, and C are independent and Find the probability .

Suppose a die is rolled twice and let A = {first toss is a prime} B = {first toss is 5} C = {second toss is a 6} D = {second toss is 5} Find the probability .

Suppose events A, B, and C are independent and Find the probability .

Quiz 13: The Nature of Probability

Suppose a slot machine has three independent wheels as shown in the figure. ​ Find the probability P(3 bar). Give your answer to four decimal places, if required. ​

What is the probability that two people in your class (assume a class of 30 students) have the same birthday? ​

Find the requested probability. ​ if ​

Suppose a slot machine has three independent wheels as shown in the figure. ​ Find the probability P(3 plum) . Round your answer to four decimal places if necessary. ​ ​

Suppose events A, B, and C are independent and , , . ​ Find the probability of . ​

Suppose events A, B, and C are independent and ​ ​ Find the probability . ​

Suppose events A, B, and C are independent and , , . ​ Find the probability of .

Suppose a die is rolled twice and let ​ A = {first toss is a prime} B = {first toss is 2} C = {second toss is a 3} D = {second toss is 2} ​ Find the probability .

Suppose that in an assortment of 6 calculators, there are 3 with defective switches. Draw with and without replacement. If two machines are selected at random, what is the probability that both have defective switches? ​

What is the probability of obtaining at least one head when a coin is flipped six times?

Suppose events A, B, and C are independent and ​ ​ Find the probability . ​

What is the probability that two people in your class (assume a class of 30 students) have the same birthday? Please, express your answer to 0.1%. ​ __________%

What is the probability of obtaining at least one head when a coin is flipped four times? ​

Which of the following is more probable? A. Flipping a coin 4 times and obtaining at least 3 heads. B. Flipping a coin 5 times and obtaining at least 3 heads.

Suppose events A, B, and C are independent and ​ ​ Find the probability .

Suppose a die is rolled twice and let ​ A = {first toss is a prime} B = {first toss is 5} C = {second toss is a 6} D = {second toss is 5} ​ Find the probability . ​

Suppose events A, B, and C are independent and ​ ​ Find the probability .

Suppose a slot machine has three independent wheels as shown in the figure. Find the probability P(3 bar). Give your answer to four decimal places, if required.

What is the probability that two people in your class (assume a class of 30 students) have the same birthday?

Find the requested probability. if

Suppose a slot machine has three independent wheels as shown in the figure. Find the probability P(3 plum) . Round your answer to four decimal places if necessary.

Suppose events A, B, and C are independent and , , . Find the probability of .

Suppose events A, B, and C are independent and Find the probability .

Suppose events A, B, and C are independent and , , . Find the probability of .

Suppose a die is rolled twice and let A = {first toss is a prime} B = {first toss is 2} C = {second toss is a 3} D = {second toss is 2} Find the probability .

Suppose that in an assortment of 6 calculators, there are 3 with defective switches. Draw with and without replacement. If two machines are selected at random, what is the probability that both have defective switches?

Suppose events A, B, and C are independent and Find the probability .

What is the probability that two people in your class (assume a class of 30 students) have the same birthday? Please, express your answer to 0.1%. __________%

What is the probability of obtaining at least one head when a coin is flipped four times?

Suppose events A, B, and C are independent and Find the probability .

Suppose a die is rolled twice and let A = {first toss is a prime} B = {first toss is 5} C = {second toss is a 6} D = {second toss is 5} Find the probability .

Suppose events A, B, and C are independent and Find the probability .