Question 1

A die is rolled 20 times and the number of twos that come up is tallied. Find the probability of getting the given result.
-More than three twos
A) .564
B) .433
C) .905
D) .403

Accepted Answer

The answer of A die is rolled 20 times and...

Question 2

A die is rolled 20 times and the number of twos that come up is tallied. Find the probability of getting the given result.
-Exactly five twos
A) .083
B) .921
C) .129
D) .003

Accepted Answer

The probability of rolling a two on a fair six-sided die is 1/6. Using the binomial probability formula, P(X=k) = (n choose k) * (p^k) * ((1-p)^(n-k)), where n=20, k=5, and p=1/6, the probability is approximately 0.129.

Question 3

A die is rolled 20 times and the number of twos that come up is tallied. Find the probability of getting the given result.
-Less than four twos
A) .364
B) .769
C) .867
D).567

Accepted Answer

The answer of A die is rolled 20 times and...

Question 4

A die is rolled 20 times and the number of twos that come up is tallied. Find the probability of getting the given result.
-More than one two
A) .005
B) .982
C).870
D) .482

Accepted Answer

The answer of A die is rolled 20 times and...

Question 5

In a certain college, $33 \%$ of the physics majors belong to ethnic minorities. Find the probability of the event from arandom sample of 10 students who are physics majors.
-Exactly 2 belong to an ethnic minority.
A).2156
B) .1990
C) .0028
D) .1929

Accepted Answer

The probability can be calculated using the binomial probability formula: $ P(X = k) = \binom{n}{k} p^k (1-p)^{n-k} $. Here, $ n = 10 $, $ k = 2 $, and $ p = 0.33 $. Plugging in these values gives the probability of exactly 2 students belonging to an ethnic minority as approximately 0.1990.

Question 6

In a certain college, $33 \%$ of the physics majors belong to ethnic minorities. Find the probability of the event from arandom sample of 10 students who are physics majors.
-Exactly 4 do not belong to an ethnic minority.
A) .2253
B) .0547
C) .2564
D) .0467

Accepted Answer

The answer of In a certain college, $33 \%$ of...

Question 7

In a certain college, $33 \%$ of the physics majors belong to ethnic minorities. Find the probability of the event from arandom sample of 10 students who are physics majors.
-Two or less belong to an ethnic minority.
A) .1080
B) .3070
C) .1990
D) .2888

Accepted Answer

The answer of In a certain college, $33 \%$ of...

Question 8

In a certain college, $33 \%$ of the physics majors belong to ethnic minorities. Find the probability of the event from arandom sample of 10 students who are physics majors.
-Seven or more belong to an ethnic minority.
A) .0032
B) .0028
C) .0185
D) .0154

Accepted Answer

The answer of In a certain college, $33 \%$ of...

Question 9

In a certain college, $33 \%$ of the physics majors belong to ethnic minorities. Find the probability of the event from arandom sample of 10 students who are physics majors.
-No more than 6 belong to an ethnic minority.
A) .0547
B) .9846
C) .9815
D) .913

Accepted Answer

The problem involves a binomial distribution with n = 10 trials and a probability of success (belonging to an ethnic minority) of p = 0.33. We need to find the probability that no more than 6 students belong to an ethnic minority, which means calculating P(X ≤ 6). Using a binomial probability table or calculator, this probability is approximately 0.9815.

Question 10

Find the requested probability.
-A child rolls a 6 -sided die 6 times. What is the probability of the child rolling exactly four fives?
A). 5360
B).3125
C) .9688
D) .0080

Accepted Answer

The probability of rolling a five on a 6-sided die is 1/6. Using the binomial probability formula for exactly four successes (rolling a five) in six trials, we calculate: P(X=4) = (6 choose 4) * (1/6)^4 * (5/6)^2 = 15 * (1/1296) * (25/36) = 0.0080.

Question 11

Find the requested probability.
-A child rolls a 6 -sided die 6 times. What is the probability of the child rolling exactly three sixes?
A) .4441
B) .5362
C) .0594
D).0536

Accepted Answer

The probability of rolling a six on a 6-sided die is 1/6. Using the binomial probability formula, the probability of rolling exactly three sixes in six rolls is calculated as: C(6,3) * (1/6)^3 * (5/6)^3 = 20 * (1/216) * (125/216) = 0.0536.

Question 12

Find the requested probability.
-A child rolls a 6-sided die 6 times. What is the probability of the child rolling exactly two fours?
A) .7182
B) .0621
C) .2009
D) .5681

Accepted Answer

The answer of Find the requested probability.
-A child rolls a...

Question 13

Find the requested probability.
-A child rolls a 6-sided die 6 times. What is the probability of the child rolling no more than three twos?
A) .6774
B) .9649
C) .9913
D) .3812

Accepted Answer

The answer of Find the requested probability.
-A child rolls a...

Question 14

Find the requested probability.
-What is the probability that 14 rolls of a fair die will show three threes?
A) .2268
B) .4536
C) .0454
D) .1134

Accepted Answer

The probability of rolling a three on a fair die is 1/6. The probability of rolling three threes in 14 rolls is (1/6)^3 * (5/6)^11 = 0.2268.

Question 15

Find the requested probability.
-What is the probability that 16 rolls of a fair die will show 5 fours?
A).0151
B) .0378
C) .1512
D) .0756

Accepted Answer

The answer of Find the requested probability.
-What is the probability...

Question 16

Find the probability of the event.
-A die is rolled 18 times and two threes come up.
A).160
B) .060
C) .099
D) .230

Accepted Answer

The answer of Find the probability of the event.
-A die...

Question 17

Find the probability of the event.
-A 10-question multiple choice test has 4 possible answers for each question. A student selects at least 6 correct answers.
A) .989
B).020
C) .118
D) .995

Accepted Answer

The probability of guessing a correct answer is 0.25. Using the binomial probability formula, the probability of getting at least 6 correct answers out of 10 is very low, approximately 0.020.

Question 18

Find the probability of the event.
-On a hospital floor, 16 patients have a disease with a mortality rate of .1. Two of them die.
A) .163
B) .275
C) .170
D) .666

Accepted Answer

The answer of Find the probability of the event.
-On a...

Question 19

Find the probability of the event.
-A battery company has found that the defective rate of its batteries is .03. Each day, 22 batteries are randomly tested. On Tuesday, 1 is found to be defective.
A).118
B).348
C) . 614
D) .110

Accepted Answer

The answer of Find the probability of the event.
-A battery...

Question 20

Decide whether or not the matrix is a probability vector.
-$\left[\begin{array}{rrr}0.3 & 0.7 & 0.7\end{array}\right]$

Accepted Answer

A probability vector must have elements that sum to 1. The elements 0.3, 0.7, and 0.7 sum to 1.7, not 1.

Quiz 9: Counting, Probability Distributions, and Further Topics in Probability

A die is rolled 20 times and the number of twos that come up is tallied. Find the probability of getting the given result. -More than three twos

A die is rolled 20 times and the number of twos that come up is tallied. Find the probability of getting the given result. -Exactly five twos

A die is rolled 20 times and the number of twos that come up is tallied. Find the probability of getting the given result. -Less than four twos

A die is rolled 20 times and the number of twos that come up is tallied. Find the probability of getting the given result. -More than one two

In a certain college, $33 \%$ of the physics majors belong to ethnic minorities. Find the probability of the event from arandom sample of 10 students who are physics majors. -Exactly 2 belong to an ethnic minority.

In a certain college, $33 \%$ of the physics majors belong to ethnic minorities. Find the probability of the event from arandom sample of 10 students who are physics majors. -Exactly 4 do not belong to an ethnic minority.

In a certain college, $33 \%$ of the physics majors belong to ethnic minorities. Find the probability of the event from arandom sample of 10 students who are physics majors. -Two or less belong to an ethnic minority.

In a certain college, $33 \%$ of the physics majors belong to ethnic minorities. Find the probability of the event from arandom sample of 10 students who are physics majors. -Seven or more belong to an ethnic minority.

In a certain college, $33 \%$ of the physics majors belong to ethnic minorities. Find the probability of the event from arandom sample of 10 students who are physics majors. -No more than 6 belong to an ethnic minority.

Find the requested probability. -A child rolls a 6 -sided die 6 times. What is the probability of the child rolling exactly four fives?

Find the requested probability. -A child rolls a 6 -sided die 6 times. What is the probability of the child rolling exactly three sixes?

Find the requested probability. -A child rolls a 6-sided die 6 times. What is the probability of the child rolling exactly two fours?

Find the requested probability. -A child rolls a 6-sided die 6 times. What is the probability of the child rolling no more than three twos?

Find the requested probability. -What is the probability that 14 rolls of a fair die will show three threes?

Find the requested probability. -What is the probability that 16 rolls of a fair die will show 5 fours?

Find the probability of the event. -A die is rolled 18 times and two threes come up.

Find the probability of the event. -A 10-question multiple choice test has 4 possible answers for each question. A student selects at least 6 correct answers.

Find the probability of the event. -On a hospital floor, 16 patients have a disease with a mortality rate of .1. Two of them die.

Find the probability of the event. -A battery company has found that the defective rate of its batteries is .03. Each day, 22 batteries are randomly tested. On Tuesday, 1 is found to be defective.

Decide whether or not the matrix is a probability vector. - $\left[\begin{array}{rrr}0.3 & 0.7 & 0.7\end{array}\right]$

Quiz 9: Counting, Probability Distributions, and Further Topics in Probability

A die is rolled 20 times and the number of twos that come up is tallied. Find the probability of getting the given result. -More than three twos

A die is rolled 20 times and the number of twos that come up is tallied. Find the probability of getting the given result. -Exactly five twos

A die is rolled 20 times and the number of twos that come up is tallied. Find the probability of getting the given result. -Less than four twos

A die is rolled 20 times and the number of twos that come up is tallied. Find the probability of getting the given result. -More than one two

In a certain college, 33%33 \%33% of the physics majors belong to ethnic minorities. Find the probability of the event from arandom sample of 10 students who are physics majors. -Exactly 2 belong to an ethnic minority.

In a certain college, 33%33 \%33% of the physics majors belong to ethnic minorities. Find the probability of the event from arandom sample of 10 students who are physics majors. -Exactly 4 do not belong to an ethnic minority.

In a certain college, 33%33 \%33% of the physics majors belong to ethnic minorities. Find the probability of the event from arandom sample of 10 students who are physics majors. -Two or less belong to an ethnic minority.

In a certain college, 33%33 \%33% of the physics majors belong to ethnic minorities. Find the probability of the event from arandom sample of 10 students who are physics majors. -Seven or more belong to an ethnic minority.

In a certain college, 33%33 \%33% of the physics majors belong to ethnic minorities. Find the probability of the event from arandom sample of 10 students who are physics majors. -No more than 6 belong to an ethnic minority.

Find the requested probability. -A child rolls a 6 -sided die 6 times. What is the probability of the child rolling exactly four fives?

Find the requested probability. -A child rolls a 6 -sided die 6 times. What is the probability of the child rolling exactly three sixes?

Find the requested probability. -A child rolls a 6-sided die 6 times. What is the probability of the child rolling exactly two fours?

Find the requested probability. -A child rolls a 6-sided die 6 times. What is the probability of the child rolling no more than three twos?

Find the requested probability. -What is the probability that 14 rolls of a fair die will show three threes?

Find the requested probability. -What is the probability that 16 rolls of a fair die will show 5 fours?

Find the probability of the event. -A die is rolled 18 times and two threes come up.

Find the probability of the event. -A 10-question multiple choice test has 4 possible answers for each question. A student selects at least 6 correct answers.

Find the probability of the event. -On a hospital floor, 16 patients have a disease with a mortality rate of .1. Two of them die.

Find the probability of the event. -A battery company has found that the defective rate of its batteries is .03. Each day, 22 batteries are randomly tested. On Tuesday, 1 is found to be defective.

Decide whether or not the matrix is a probability vector. - [0.30.70.7]\left[\begin{array}{rrr}0.3 & 0.7 & 0.7\end{array}\right][0.3​0.7​0.7​]

In a certain college, $33 \%$ of the physics majors belong to ethnic minorities. Find the probability of the event from arandom sample of 10 students who are physics majors. -Exactly 2 belong to an ethnic minority.

In a certain college, $33 \%$ of the physics majors belong to ethnic minorities. Find the probability of the event from arandom sample of 10 students who are physics majors. -Exactly 4 do not belong to an ethnic minority.

In a certain college, $33 \%$ of the physics majors belong to ethnic minorities. Find the probability of the event from arandom sample of 10 students who are physics majors. -Two or less belong to an ethnic minority.

In a certain college, $33 \%$ of the physics majors belong to ethnic minorities. Find the probability of the event from arandom sample of 10 students who are physics majors. -Seven or more belong to an ethnic minority.

In a certain college, $33 \%$ of the physics majors belong to ethnic minorities. Find the probability of the event from arandom sample of 10 students who are physics majors. -No more than 6 belong to an ethnic minority.

Decide whether or not the matrix is a probability vector. - $\left[\begin{array}{rrr}0.3 & 0.7 & 0.7\end{array}\right]$