Question 1

Sue Anne owns a medium-sized business.The probability model below describes the number of employees that may call in sick on any given day. 
What is the expected value of the number of employees calling in sick each day?

Accepted Answer

The expected value is calculated by adding the products of each possible outcome and its corresponding probability. E(X) = 0.1(0) + 0.35(1) + 0.4(2) + 0.1(3) = 1.65, so the correct choice is (C).

Question 2

Hugh buys $8,000 worth of stock in an electronics company which he hopes to sell afterward at a profit.The company is developing a new laptop computer and a new desktop computer.If it releases both computers before its competitor,the value of Hugh's stock will jump to $21,000.If it releases one of the computers before its competitor,the value of Hugh's stock will jump to $17,000.If it fails to release either computer before its competitor,Hugh's stock will be worth only $5,000.Hugh believes that there is a 40% chance that the company will release the laptop before its competitor and a 50% chance that the company will release the desktop before its competitor.Create a probability model for Hugh's profit.Assume that the development of the laptop and the development of the desktop are independent events.

Accepted Answer

We can create a probability tree diagram to visualize the various outcomes and their probabilities:

```
              / Laptop before Competitor (0.4) -- Value = $21,000
             /
            / 
Initial ---  
            \ 
             \
              \ Desktop before Competitor (0.5) -- Value = $17,000
               \
                \
                 \ Neither before Competitor (0.1) -- Value = $5,000
```

Using this probability tree, we can calculate the expected value of Hugh's stock:

Expected value = (0.4 * $21,000) + (0.5 * $17,000) + (0.1 * $5,000) = $16,300

Therefore, the best choice is B, which is the closest to the expected value of $16,300.

Question 3

A company bids on two contracts.It anticipates a profit of $50,000 if it gets the larger contract and a profit of $10,000 if it gets the smaller contract.It estimates that there's a 10% chance of winning the larger contract and a 70% chance of winning the smaller contract.Create a probability model for the company's profit.Assume that the contracts will be awarded independently.

Accepted Answer

A

Question 4

An insurance policy costs $400,and will pay policyholders $10,000 if they suffer a major injury (resulting in hospitalization),or $2,000 if they suffer a minor injury (resulting in lost time from work).The company estimates that each year 1 in every 3,000 policyholders may have a major injury,and 1 in 1,000 a minor injury.Create a probability model for the company's profit on this policy.

Accepted Answer

The answer of An insurance policy costs $400,and will pay...

Question 5

The probability model below describes the number of thunderstorms that a certain town may experience during the month of August. 
How many storms can the town expect each August?

Accepted Answer

The answer of The probability model below describes the number...

Question 6

You roll a fair die.If you get a number greater than 4,you win $70.If not,you get to roll again.If you get a number greater then 4 the second time,you win $30.Otherwise you win nothing.
Create a probability model for the amount you win at this game.

Accepted Answer

The answer of You roll a fair die.If you get...

Question 7

You pick a card from a deck.If you get a face card,you win $5.If you get an ace,you win $30 plus an extra $50 for the ace of hearts.For any other card you win nothing.
Create a probability model for the amount you win at this game.

Accepted Answer

The probability of getting a face card is 12/52, which simplifies to 3/13. The probability of getting an ace is 4/52, which simplifies to 1/13. The probability of getting the ace of hearts is 1/52. For any other card, the probability is 36/52, which simplifies to 9/13. 
Therefore, the probability model for the amount you win at this game is as follows:
- You win $5 with probability 3/13
- You win $30 + $50 with probability 1/52
- You win nothing with probability 9/13.

Question 8

The number of golf balls ordered by customers of a pro shop has the following probability distribution.

Accepted Answer

The answer of The number of golf balls ordered by...

Question 9

You pick a card from a deck.If you get a club,you win $80.If not,you get to draw again (after replacing the first card).If you get a club the second time,you win $30.Otherwise you win nothing.
Create a probability model for the amount you win at this game.

Accepted Answer

The probability model for the amount you win can be represented as:

- Probability of drawing a club on the first attempt = 13/52 = 1/4 (since there are 13 clubs in a standard deck of 52 cards)
- Winning amount on the first attempt = $80
- Probability of not drawing a club on the first attempt = 1 - 1/4 = 3/4
- Probability of drawing a club on the second attempt = 13/52 x 3/4 x 13/52 = 169/832
- Winning amount on the second attempt = $30
- Probability of not drawing a club on the second attempt = 1 - 169/832 = 663/832
- Winning amount in this case = $0

Therefore, the probability model is:

- $80 with probability 1/4
- $30 with probability 169/832
- $0 with probability 663/832

Option C has the correct probability model and is therefore the best choice.

Question 10

A couple plans to have children until they get a boy,but they agree that they will not have more than four children even if all are girls.
Create a probability model for the number of children they will have.Assume that boys and girls are equally likely.

Accepted Answer

The answer of A couple plans to have children until...

Question 11

A carnival game offers a $80 cash prize for anyone who can break a balloon by throwing a dart at it.It costs $5 to play and you're willing to spend up to $20 trying to win.You estimate that you have an 10% chance of hitting the balloon on any throw.Create a probability model for the number of darts you will throw.Assume that throws are independent of each other.Round to four decimal places if necessary.

Accepted Answer

The answer of A carnival game offers a $80 cash...

Question 12

Jo is a hairstylist.The probability model below describes the number of clients that she may see in a day. 
What is the expected value of the number of clients that Jo sees per day?

Accepted Answer

To find the expected value, we multiply each possible number of clients she may see by its corresponding probability, and then take the sum of all these products. 
Expected value = (0.1 * 0) + (0.3 * 1) + (0.4 * 2) + (0.2 * 3) + (0.1 * 4) = 0 + 0.3 + 0.8 + 0.6 + 0.4 = 2.80. So the expected value of clients that Jo sees per day is 2.80. The answer is D.

Question 13

Accepted Answer

There is only one item mentioned in the image and it has a rating of 3.6 out of 5 stars. Converting this to a fraction gives 0.72, which is closest to 0.6 (option D) when rounded to one decimal place.

Question 14

Accepted Answer

The answer of 
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Question 15

Accepted Answer

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Question 16

The accompanying table describes the probability distribution for the number of adults in a certain town (among 4 randomly selected adults)who have a college degree.

Accepted Answer

The answer of The accompanying table describes the probability distribution...

Question 17

A carnival game offers a $80 cash prize for anyone who can break a balloon by throwing a dart at it.It costs $5 to play and you're willing to spend up to $20 trying to win.You estimate that you have a 12% chance of hitting the balloon on any throw.Create a probability model for the amount you will win.Assume that throws are independent of each other.Round to four decimal places if necessary.

Accepted Answer

The answer of A carnival game offers a $80 cash...

Question 18

You roll a pair of fair dice.If you get a sum greater than 10 you win $50.If you get a double you win $40.If you get a double and a sum greater than 10 you win $90.Otherwise you win nothing.
Create a probability model for the amount you win at this game.

Accepted Answer

The answer of You roll a pair of fair dice.If...

Question 19

Accepted Answer

The product code "TB3448_00" does not provide any relevant information regarding the answer choices. Therefore, the answer can only be obtained by looking at the given options themselves. Option C (220) is the closest to an average of the other options (240, 250, 200, and 150), making it the best choice.

Question 20

Accepted Answer

The answer of 
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Quiz 15: Random Variables

Sue Anne owns a medium-sized business.The probability model below describes the number of employees that may call in sick on any given day. What is the expected value of the number of employees calling in sick each day?

The probability model below describes the number of thunderstorms that a certain town may experience during the month of August. How many storms can the town expect each August?

You roll a fair die.If you get a number greater than 4,you win $70.If not,you get to roll again.If you get a number greater then 4 the second time,you win $30.Otherwise you win nothing. Create a probability model for the amount you win at this game.

You pick a card from a deck.If you get a face card,you win $5.If you get an ace,you win $30 plus an extra $50 for the ace of hearts.For any other card you win nothing. Create a probability model for the amount you win at this game.

The number of golf balls ordered by customers of a pro shop has the following probability distribution.

You pick a card from a deck.If you get a club,you win $80.If not,you get to draw again (after replacing the first card) .If you get a club the second time,you win $30.Otherwise you win nothing. Create a probability model for the amount you win at this game.

A couple plans to have children until they get a boy,but they agree that they will not have more than four children even if all are girls. Create a probability model for the number of children they will have.Assume that boys and girls are equally likely.

Jo is a hairstylist.The probability model below describes the number of clients that she may see in a day. What is the expected value of the number of clients that Jo sees per day?

The accompanying table describes the probability distribution for the number of adults in a certain town (among 4 randomly selected adults) who have a college degree.

You roll a pair of fair dice.If you get a sum greater than 10 you win $50.If you get a double you win $40.If you get a double and a sum greater than 10 you win $90.Otherwise you win nothing. Create a probability model for the amount you win at this game.