problem set-2

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 1.8x10-8). There are no other prizes, so the probability of winning nothing = 1 – (1.8x10-8) = 0.999999982. The probability model is:

Winnings (X)

0

$10 x 106

P(X = xi)

0.999999982

1.8 x 10-8

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?