a. Create a probability model for the random variable X = cost of claims. b. What is the long-term average cost the retailer should expect to pay to its customers per claim? C. With what standard deviation?
Chapter 15 CW #1 - Probability Models (Random Variables)
1.
An electronics retailer is developing a model for insurance policies on new cell phone purchases. It
estimates that 60% of customers never make a claim, 25% of customers require a small repair costing an
average of $50, and 15% of customers request a full refund costing $200.
a. Create a probability model for the random variable X = cost of claims.
b.
What is the long-term average cost the retailer should expect to pay to its customers per claim?
C.
With what standard deviation?
2. A commuter must pass through four traffic lights on her way to work and will have to stop at each one that
is red. She estimates the probability model for the number of red lights she hits, as shown.
X
0
P(x)
0.10 0.25
2
3
0.15
0.15
a. Define the random variable.
b. Finish the table above.
c. How many red lights should she expect to hit each day?
d. What is the standard deviation?
3. You draw a card from a deck. If you get a red card, you win nothing. If you get a spade, you win $5. For any
club, you win $10 plus and extra $20 for the ace of clubs.
a. Define the random variable. X.
b. Create a probability model for the amount you win.
C
What is the expected amount you'll win?
d.
Find the standard deviation.
4.
Mary is deciding whether to book the cheaper flight home from college after her final exams, but she's
unsure when her last exam will be. She thinks there is only a 20% chance that the exam will be scheduled
after the last day she can get a seat on the cheaper flight. If it is and she must cancel her flight, she will
lose $150. If she can take the cheaper flight, she will save $100.
a. Create a probability model for the amount Mary can save for her flight.
b. If she books the cheaper flight, how much can she expect to gain?
c. What is the standard deviation?
d. Write answers (b) and (c) in context.
5. A couple plans to have children until they get a girl, but they agree that they will not have more than three
children even if all are boys. (Assume boys and girls are equally likely.)
a. Create a probability model for the number of children they might have.
b. Find the expected number of children.
c. Find the standard deviation.
6. You play two games against the same opponent. The probability you win the first game is 0.4. if you win
the first game, the probability you also win the second is 0.2. if you lose the first game, the probability that
you win the second is 0.3.
a. Are the two games independent? Explain.
b. Draw a tree diagram to represent the outcomes. Label the branches with values.
c. What's the probability you lose both games?
d. What's the probability you win both games.
e. Let the random variable X be the number of games you win. Find the probability model for X.
f.
What are the expected value and standard deviation?
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