1. a. Assuming that the probability of having a girl is .5, what is the probability of having a boy? How do you know?
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1. b. My husband and I are planning to have three children. What is the probability that we will have two girls and a boy? (Show your work on a separate page.)
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1.c. We've already had two of our three children (a boy and a girl). What is the probability that we will end up with two girls and a boy?
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1.d. Explain the relationship between your answers to problems 1.b. and 1.c.
2. Joe is on trial for murder. There is a 70% chance that he will be convicted. If he is convicted, there is a 90% chance that he will be sentenced to death. What is the probability that he will be sentenced to death? (Show your work on a separate sheet.)
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Expected Value: Expected value is the value we attach to something that may or may not come to fruition. For example, if I buy a lottery ticket that has a 20% chance of paying $100, the expected value of the lottery ticket is .2 (the probability of the ticket paying) x $100 (the potential payout) ... this means that the expected value of the ticket is .2x100 = $20. If I can buy the ticket for $10, I should buy it! I'm getting a ticket with an expected value of $20 for only $10 (a bargain). If, however, the ticket costs $25, I shouldn't buy the ticket ... even though I could win $100.
3. Given that explanation of expected value, consider the following situation. You are a lawyer for a guy named Stu. Stu has been charged with armed robbery. Stu has been offered a plea deal: he pleads guilty and will be sentenced to 5 years in prison, end of story. Given your past experience, you believe there is only a 40% chance that Stu will be found guilty if he goes to trial, but if he is found guilty, he will be sentenced to 20 years in prison.
a. What is the "expected value" of the plea deal (in terms of prison time)?
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b. What is the "expected value" of going to trial (in terms of prison time)?
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c. As a good lawyer, what do you recommend to Stu? Explain.