a) Suppose that X is a binomial random variable with n = 70 and p = 0.3. i. Compute the exact probability that X is less than 3. ii. Approximate the probability that X is less than 3 and compare to the result in part (i). iii. Approximate the probability that 8< x <12.

Assume that the probability that an airplane engine will fail during a torture test is 12and that the aircraft in question has 4 engines. Construct a sample space for the torture test. Use S for survive and F for fail.

Find the probability of each event. Drawing 5 orange cubes from a bowl containing 5 orange cubes and 1 beige cubes

On a game show, a contestant is given the digits 3, 4, and 5 to arrange in the proper order to form the price of an appliance. If the contestant is correct, he or she wins the appliance. What is the probability of winning when the contestant knows that the price is at least $400?