Question 1

Can the vector  be a probability vector?

Accepted Answer

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

Question 2

Can the matrix  be a transition matrix?

Accepted Answer

A transition matrix must have entries that represent probabilities, which means they must be non-negative and add up to 1 in each row. The given matrix consists of arbitrary hexadecimal values and does not satisfy these requirements, so it cannot be a transition matrix.

Question 3

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 4

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

There are two parts to this problem. First, we need to determine the number of ways to select exactly one minority candidate out of four, and second, we need to determine the number of ways to select seven non-minority candidates out of ten.

The number of ways to select exactly one minority candidate out of four is C(4,1) = 4.

The number of ways to select seven non-minority candidates out of ten is C(10,7) = 120.

The total number of ways to select eight people out of fourteen is C(14,8) = 3003.

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

P = (number of ways to select one minority candidate) × (number of ways to select seven non-minority candidates) / (total number of ways to select eight people)

P = (4 × 120) / 3003 ≈ 0.1592

Rounded to four decimal places, the answer is 0.1592, which corresponds to choice C.

Question 5

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 6

A box of 27 transistors contains 7 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 27 transistors contains 7...

Question 7

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 8

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

There are 10 people in the group, so there are 10C3 ways to choose 3 finalists. There are 6 men in the group, so there are 6C3 ways to choose 3 men. Therefore, the probability of choosing 3 men is 6C3 / 10C3 = 20 / 120 = 1 / 6 = 0.167.

Question 9

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 10

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 11

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...

Question 12

A car dealer has 15 different cars that he would like to display, but he has room to display only 3. Suppose 11 of the cars are the same color, with the remaining 4 having different colors that are distinct from each other. If the dealer tells a salesperson to display any 3 cars, what is the probability that all 3 cars will be the same color? ​

Accepted Answer

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

Question 13

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 14

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 draw is 7/11. 
After one defective transistor is drawn, there are 6 defective transistors left in a box of 10 transistors.
Therefore, the probability of drawing another defective transistor on the second draw is 6/10.
The probability of both events happening together is:
(7/11) x (6/10) = 42/110 = 0.38 (rounded to two decimal places).
Therefore, the correct choice is B.

Question 15

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 16

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

The number of ways to pick 4 cars out of 7 is given by the combination formula: C(7,4) = 7!/4!(7-4)! = 35. Therefore, the correct answer is (D) 35.

Question 17

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 total number of ways to select six people from nine is $\binom{9}{6}=84$. The number of ways to select all two minority candidates and any four of the remaining seven candidates is $\binom{2}{2} 	imes \binom{7}{4}=21$. So the probability that all two minority candidates are hired is $\dfrac{21}{84}=\boxed{0.250000}$.

Question 18

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 total number of possible hands that can be dealt from a deck of 52 cards is
52C26 = (52!)/(26!26!) = 495,918,532,948,104.

The number of hands that contain 5 spades, 10 hearts, 9 diamonds, and 6 clubs is the product of the number of ways to choose 5 spades, 10 hearts, 9 diamonds, and 6 clubs from their respective suits, which is:

(13C5)(13C10)(13C9)(13C6) = (1,287,084)(196,125)(86,365)(13,275) = 582,353,255,604,953,125.

Therefore, the probability of being dealt a hand containing 5 spades, 10 hearts, 9 diamonds, and 6 clubs is:

582,353,255,604,953,125 / 495,918,532,948,104 ≈ 0.0017

Therefore, the best choice is D.

Question 19

Can the vector  be a probability vector? ​

Accepted Answer

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

Question 20

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 of selecting 5 claims out of 40 is given by the combination formula:

C(40,5) = 40!/(5!35!) = 40*39*38*37*36/(5*4*3*2*1) = 658008

The probability of selecting no fraudulent claims out of the 37 non-fraudulent claims is:

C(37,5) = 37!/(5!32!) = 37*36*35*34*33/(5*4*3*2*1) = 376992

Therefore, the probability of selecting none of the fraudulent claims is:

P = 376992/658008 = 0.662 (rounded to three decimal places)

So, the best choice is C.

Quiz 8: Introduction to Probability

Can the vector be a probability vector?

Can the matrix be a transition matrix?

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 box of 27 transistors contains 7 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.

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. ​

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. ​

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? ​

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. ​

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? ​

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. ​

Can the vector be a probability vector? ​

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 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.

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.

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?

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.

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?

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.

Can the vector be a probability vector?