USA Today reports that about 25% of all prison parolees become repeat offenders. Alice is a social worker whose job is to counsel people on parole. Let us say success means a person does not become a repeat offender. Alice has been given a group of four parolees. (a) Find the probability P(r) of r successes ranging from 0 to 4. (Round your answers to three decimal places.) P(0) = P(1) = P(2) = P(3) = P(4) = (b) What is the expected number of parolees in Alice's group who will not be repeat offenders? parolees What is the standard deviation? (Round your answer to two decimal places.) parolees (c) What is the smallest group Alice can counsel to be at least 98% sure that three or more parolees will not become repeat offenders? parolees

Your car is making a funny noise. You believe that the problem is either with the wheel or the axle, and you believe the probability is 0.3 that the wheel needs to be replaced, and 0.7 that the axle needs to be replaced. You need to decide whether to replace the wheel or the axle first. The cost of each alternative is given in the following table (if you decided to replace the wrong part first, you have to replace both of them). The Wheel is broken p = 0.3 The Axle is broken p = 0.7 Replace Wheel First Replace Axle First 600 1500 1500 900 a) Find the EV of each decision alternative. Which part should you replace first? b) What is the EVPI?

Suppose you are deciding whether or not to bring an umbrella to school and the weathercan be either sunny or rainy. Initially, you think the probability that it will be sunny isP (S) = 0.6, and the probability that it will be rainy is P (R) = 0.4. If you bring an umbrellaand it rains, your payoff is 6. If you bring an umbrella and it is sunny, your payoff is 9. Ifyou don’t bring an umbrella and it rains, your payoff is 0. If you don’t bring an umbrellaand it is sunny, your payoff is 10. Suppose that you check two websites for weather forecasts.You know that the two forecasts are independent of each other, and each forecast is correct70% of the time. That is, the probability that the website says it will be sunny given that itactually will be sunny is 0.7, and the probability that the website says it will rain given thatit actually will rain is 0.7. Suppose that you suffer from confirmation bias. You initially thinkit is more likely to be sunny, so you misinterpret rain forecasts as sun…

You purchase a brand new car for $15,000 and insure it. The policy pays 78% of the car's value if there is an issue with the engine or 30% of the car's value if there is an issue with the speaker system. The probability of an issue with the engine is 0.009, and the probability there is an issue with the speaker system is 0.02. The premium for the policy is p. Let X be the insurance company's net gain from this policy. (a) Create a probability distribution for X, using p to represent the premium on the policy. Enter the possible values of X in ascending order from left to right. P(X) (b) Compute the minimum amount the insurance company will charge for this policy. Round your answer to the nearest cent