Use a calculator or computer to find the probability that x = 2 in a binomial experiment where n = 11 and p = 0.29. (Give your answer correct to four decimal places.) P(x = 2 | B(11, 0.29)) = .........

The annual premium for a $20,000 insurance policy against the theft of a painting is $350. If the (empirical) probability that the painting will be stolen during the year is 0.02, what is your expected return from the insurance company if you take out this insurance? Let X be the random variable for the amount of money received from the insurance company in the given year. E(X)= dollars

Suppose you are given the following facts. For a given disease, there is a test which is 80% reliable (Pr(Y|D) = .8). How high does the base rate for the disease need to be for the probability of a false positive to be 20%?

T15 Suppose that 90% of drivers are "careful" and 10% are "reckless." Suppose further that a careful driver has a 0.2 probability of being in an accident in a given year, while for a reckless driver the probability is 0.4. What is the probability that a randomly selected driver will have an accident within a year? (Enter your answer to two decimal places.)