In a particular state, 90% of murderers are male, and 70% of these murderers kill males. Female killers also tend to kill men4 out of 5 kill men. The likelihood of receiving a life sentence varies by gender combination according to the table below (e.g., the probability that a male offender who killed a male victim is sentenced to life is .70.):
|
Offender Sex |
Victim Sex |
Probability of a life sentence |
|
Male |
Male |
0.70 |
|
Male |
Female |
0.90 |
|
Female |
Male |
0.10 |
|
Female |
Female |
0.20 |
a. What is the probability that a randomly selected lifer is male?
b. What is the probability that a randomly selected lifer killed a female?
c. What is the probability that a randomly selected lifer Is male or killed a female?
d. What is the probability that a randomly selected lifer Is male and killed a female?
e. What is the probability of male killers being sentenced to life?
f. What is the probability of female killers being sentenced to life?
g. What is the probability that a randomly selected killer is sentenced to life?
4. Suppose that 90% of adults get married at least once, that 40% of first marriages end in divorce, that 70% of those marry for the second time, that 50% of second marriages end in divorce, that 35% of the double divorcees marry for the third time, that 75% of third marriages end in divorce, that 10% of those marry a fourth time, and for them the fourth time is a charm as 80% say with their fourth spouse. For a population of 1,000 people, how many marriages and how many divorces would you expect?
6. Professors Smith, Jones and I, all wanting to teach a particular course have agreed to fight it out with a trial (a three-cornered version of a dual). The rules are as follows. We will each take a shot in rotation–first me (I made up the rules), then Smith, and then Jones. This continues until only one of us remains standing. On each turn, the shooter can decide on his target. Now, given my poor eyesight, Im not that good of a marksman (As and Bs yes, guns and ammo definitely not). They call me dead eye, but they mean it literally. My probability of hitting the target is only .30; P(F) = P(Fox hitting target) = .30. Smith is a perfect shot, P(S) = P(Smith hitting target) = 1.0, having a 100% chance of hitting his target. Finally, Jones shoots 50/50, that is P(J) = P(Jones hitting target) = .50. Given this scenario, what is my best strategy and why? (Note: This is a particularly challenging, extra credit problem).
