**IHP 525 Module Three Problem Set**

1. What is the probability of being born on:

a) February 28?

b) February 29?

c) February 28 or February 29?

2. A patient newly diagnosed with a serious ailment is told he has a 60% probability of surviving 5 or more years. Let us assume this statement is accurate. Explain the meaning of this statement to someone with no statistical background in terms he or she will understand.

3. A lottery offers a grand prize of $10 million. The probability of winning this grand prize is 1 in 55 million (about 1.8×10^{-8}). There are no other prizes, so the probability of winning nothing = 1 – (1.8×10^{-8}) = 0.999999982. The probability model is:

Winnings ( |
0 |
$10 x 10 |

P( |
0.999999982 |
1.8 x 10 |

a) What is the expected value of a lottery ticket?

b) Fifty-five million lottery tickets will be sold. How much does the proprietor of the lottery need to charge per ticket to make a profit?

4. Suppose a population has 26 members identified with the letters A through Z.

a) You select one individual at random from this population. What is the probability of selecting individual A?

b) Assume person A gets selected on an initial draw, you replace person A into the sampling frame, and then take a second random draw. What is the probability of drawing person A on the second draw?

c) Assume person A gets selected on the initial draw and you sample again without replacement. What is the probability of drawing person A on the second draw?

5. Let A represent cat ownership and B represent dog ownership. Suppose 35% of households in a population own cats, 30% own dogs, and 15% own both a cat and a dog. Suppose you know that a household owns a cat. What is the probability that it also owns a dog?

6. What is the complement of an event?

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