Question 1

An insurance company receives 40 claims in a certain month. Company policy mandates that a random selection of 5 of these claims be thoroughly investigated. If 3 of the 40 claims are fraudulent, find the probability that none of the fraudulent claims are thoroughly investigated. Round your answer to three decimal places. ​

Accepted Answer

The probability that none of the fraudulent claims are investigated is calculated by choosing 5 claims out of the 37 non-fraudulent ones, divided by the total ways to choose 5 claims out of 40. This is calculated as (37 choose 5) / (40 choose 5) = 0.662.

Question 2

A box of 11 transistors has 7 defective ones. If 2 transistors are drawn from the box together, what is the probability that both transistors are defective? Round your answer to two decimal places. ​

Accepted Answer

The probability of drawing a defective transistor on the first attempt is 7/11.
After drawing one defective transistor, there will be 6 defective transistors left out of 10 transistors total.
Thus, the probability of drawing another defective transistor on the second attempt is 6/10.
Using the multiplication rule of probability, the probability of drawing 2 defective transistors in sequence is (7/11) * (6/10) = 0.38 which rounded to two decimal places is 0.38.
Therefore, the best choice is B.

Question 3

Six men and four women are semifinalists in a lottery. From this group, three finalists are to be selected by a drawing. What is the probability that all four finalists will be men? Round your answer to three decimal places. ​

Accepted Answer

The question mistakenly asks for the probability of selecting four finalists when only three are to be chosen. Assuming the question meant to ask for the probability of all three finalists being men: The total ways to choose 3 finalists out of 10 semifinalists is 10C3 = 120. The ways to choose 3 men out of 6 is 6C3 = 20. So, the probability is 20/120 = 0.167. However, none of the provided options match this corrected calculation, suggesting a misunderstanding in the question's phrasing or in the calculation process. Given the options, none directly align with the corrected calculation, but the closest process (assuming a typo in the question or answer choices) would lead to an answer not listed accurately according to the standard calculation.

Question 4

A box of 26 transistors has 3 defective ones. If 2 transistors are drawn from the box together, what is the probability that neither transistor is defective? Round your answer to four decimal places. ​

Accepted Answer

The answer of A box of 26 transistors has 3...

Question 5

A box of 22 transistors contains 6 that are defective. If 2 transistors are drawn from the box together, what is the probability that exactly one of the two transistors is defective? Round your answer to four decimal places. ​

Accepted Answer

The answer of A box of 22 transistors contains 6...

Question 6

Find the probability of being dealt a hand containing 5 spade, 10 hearts, 9 diamonds, and 6 clubs. Assume that a normal deck of 52 cards is used. Round your answer to four decimal places. ​

Accepted Answer

The probability of being dealt a specific hand of 30 cards (5 spades, 10 hearts, 9 diamonds, and 6 clubs) out of a deck of 52 cards is given by the hypergeometric probability distribution:

P(X=30) = (5 choose 5)(10 choose 10)(9 choose 9)(6 choose 6)/(52 choose 30)

Simplifying this expression, we get:

P(X=30) = 1/292759492173

Rounding to four decimal places, we get 0.0017. Therefore, the answer is D.

Question 7

As a reward for a record year, the Ace Software Company is randomly selecting 5 people from its 70 employees for a free trip to Hawaii, but it will not pay for a traveling companion. If John and Jill are married and both are employees, what is the probability that they will both win? Round your answer to five decimal places. ​

Accepted Answer

The answer of As a reward for a record year,...

Question 8

What is the probability of being dealt a poker hand of 5 cards containing exactly 5 cards of the same suit? Round your answer to six decimal places. ​

Accepted Answer

The answer of What is the probability of being dealt...

Question 9

A car dealer has 7 different cars that he would like to display, but he has room to display only 4. In how many ways can he pick 4 cars to display? ​

Accepted Answer

This problem involves finding the number of combinations of 4 cars that can be selected out of 7, which is given by the formula 7C4 = (7*6*5*4)/(4*3*2*1) = 35. Therefore, the best choice is D.

Question 10

Suppose that an employer plans to hire six people from a group of nine equally qualified people, of whom two are minority candidates. If the employer does not know which candidates are minority candidates, and if she selects her employees at random, what is the probability that all two minority candidates are hired? Round your answer to six decimal places. ​

Accepted Answer

The answer of Suppose that an employer plans to hire...

Question 11

In one state there is a lottery game called Pick 4. The state chooses 12 numbers from 46 numbers, and each player chooses 4 numbers from the same 46 numbers. If all 4 of a player's numbers are among the 12 numbers that the state picked, then that player is a "big winner." Find the probability of being a big winner. Round your answer to four decimal places. ​

Accepted Answer

The answer of In one state there is a lottery...

Question 12

In a 10-question matching test with 10 possible answers to match and no answer used more than once, what is the probability of guessing and getting every answer correct? ​

Accepted Answer

The answer of In a 10-question matching test with 10...

Question 13

What is the probability of being dealt a poker hand of 5 cards containing exactly 4 spades? Round your answer to two decimal places. ​

Accepted Answer

The answer of What is the probability of being dealt...

Question 14

To see whether a bank has enough minority construction company loans, a social agency selects 31 loans to construction companies at random and finds that 4 of them are loans to minority companies. If the bank's claim that 10 of every 100 of its loans to construction companies are minority loans is true, what is the probability that 4 loans out of 31 are minority loans? Leave your answer with combination symbols. ​

Accepted Answer

The answer of To see whether a bank has enough...

Question 15

Suppose that an employer plans to hire eight people from a group of fourteen equally qualified people, of whom four are minority candidates. If the employer does not know which candidates are minority candidates, and if she selects her employees at random, what is the probability that exactly one minority candidate is hired? Round your answer to four decimal places. ​

Accepted Answer

We first find the total number of ways to select 8 people from a group of 14 equally qualified people:

${{14}\choose{8}} = 3003$

Next, we find the number of ways to select exactly one minority candidate and seven non-minority candidates:

$({{4}\choose{1}} \cdot {{10}\choose{7}}) = 1200$

We multiply this by the number of ways to arrange these 8 people (since the order in which they are hired doesn't matter) which is $8!$.

So the total number of ways to select exactly one minority candidate and seven non-minority candidates and arrange them is:

$( {{4}\choose{1}} \cdot {{10}\choose{7}} ) \cdot 8! = 1200 \cdot 40,320 = 48,384,000$

Thus, the probability of selecting exactly one minority candidate is:

$\frac{48,384,000}{3003} \approx 0.1603$

Rounding to four decimal places, we get 0.1603, which corresponds to choice C.

Question 16

Suppose that five of the eight students running for class officers (president, vice president, secretary, and treasurer) have grade-point averages (GPAs) above 3.0. If the officers are selected at random, what is the probability that all four officers will be students with GPAs above 3.0? ​

Accepted Answer

The answer of Suppose that five of the eight students...

Question 17

Suppose that an employer plans to hire four people from a group of eleven equally qualified people, of whom three are minority candidates. If the employer does not know which candidates are minority candidates, and if she selects her employees at random, what is the probability that no minority candidates are hired? Round your answer to two decimal places. ​

Accepted Answer

The answer of Suppose that an employer plans to hire...

Question 18

Can the vector  be a probability vector?
​

Accepted Answer

The answer of Can the vector  be a probability...

Question 19

A car dealer has 15 different cars that he would like to display, but he has room to display only 5. Suppose 9 of the cars are the same color, with the remaining 6 having different colors that are distinct from each other. If the dealer tells a salesperson to display any 5 cars, what is the probability that all 5 cars will be the same color? ​

Accepted Answer

The answer of A car dealer has 15 different cars...

Question 20

A retailer purchases 140 of a new brand of DVD player, of which 4 are defective. The purchase agreement says that if he tests 8 chosen at random and finds 1 or more defective, he receives all the DVD players free of charge. What is the probability that he will not have to pay for the DVD players? Round your answer to three decimal places. ​

Accepted Answer

The answer of A retailer purchases 140 of a new...

Quiz 7: Introduction to Probability

A box of 11 transistors has 7 defective ones. If 2 transistors are drawn from the box together, what is the probability that both transistors are defective? Round your answer to two decimal places. ​

Six men and four women are semifinalists in a lottery. From this group, three finalists are to be selected by a drawing. What is the probability that all four finalists will be men? Round your answer to three decimal places. ​

A box of 26 transistors has 3 defective ones. If 2 transistors are drawn from the box together, what is the probability that neither transistor is defective? Round your answer to four decimal places. ​

A box of 22 transistors contains 6 that are defective. If 2 transistors are drawn from the box together, what is the probability that exactly one of the two transistors is defective? Round your answer to four decimal places. ​

Find the probability of being dealt a hand containing 5 spade, 10 hearts, 9 diamonds, and 6 clubs. Assume that a normal deck of 52 cards is used. Round your answer to four decimal places. ​

What is the probability of being dealt a poker hand of 5 cards containing exactly 5 cards of the same suit? Round your answer to six decimal places. ​

A car dealer has 7 different cars that he would like to display, but he has room to display only 4. In how many ways can he pick 4 cars to display? ​

In a 10-question matching test with 10 possible answers to match and no answer used more than once, what is the probability of guessing and getting every answer correct? ​

What is the probability of being dealt a poker hand of 5 cards containing exactly 4 spades? Round your answer to two decimal places. ​

Suppose that five of the eight students running for class officers (president, vice president, secretary, and treasurer) have grade-point averages (GPAs) above 3.0. If the officers are selected at random, what is the probability that all four officers will be students with GPAs above 3.0? ​

Can the vector be a probability vector? ​

A box of 11 transistors has 7 defective ones. If 2 transistors are drawn from the box together, what is the probability that both transistors are defective? Round your answer to two decimal places.

Six men and four women are semifinalists in a lottery. From this group, three finalists are to be selected by a drawing. What is the probability that all four finalists will be men? Round your answer to three decimal places.

A box of 26 transistors has 3 defective ones. If 2 transistors are drawn from the box together, what is the probability that neither transistor is defective? Round your answer to four decimal places.

A box of 22 transistors contains 6 that are defective. If 2 transistors are drawn from the box together, what is the probability that exactly one of the two transistors is defective? Round your answer to four decimal places.

Find the probability of being dealt a hand containing 5 spade, 10 hearts, 9 diamonds, and 6 clubs. Assume that a normal deck of 52 cards is used. Round your answer to four decimal places.

What is the probability of being dealt a poker hand of 5 cards containing exactly 5 cards of the same suit? Round your answer to six decimal places.

A car dealer has 7 different cars that he would like to display, but he has room to display only 4. In how many ways can he pick 4 cars to display?

In a 10-question matching test with 10 possible answers to match and no answer used more than once, what is the probability of guessing and getting every answer correct?

What is the probability of being dealt a poker hand of 5 cards containing exactly 4 spades? Round your answer to two decimal places.

Suppose that five of the eight students running for class officers (president, vice president, secretary, and treasurer) have grade-point averages (GPAs) above 3.0. If the officers are selected at random, what is the probability that all four officers will be students with GPAs above 3.0?

Can the vector be a probability vector?