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IHP 525 Module Three Problem Set1. 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 (X)0$10 x 106P(X = xi)0.9999999821.8 x 10-8a) 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?