Dan's Diner employs three dishwashers. Al washes 40% of the dishes and breaks only 2% of those he handles. Betty and Chuck each wash 30% of the dishes, and Betty breaks only 2% of hers, but Chuck breaks 4% of the dishes he washes. You go to Dan's for supper one night and hear a dish break at the sink. What's the probability that Chuck is on the job? The probability that Chuck is on the job is. (Round to three decimal places as needed.)

Four people buy raffle tickets and place all of their tickets into a hat.  Raphael bought 8 tickets, Leonardo bought 3 tickets, Michelangelo bought 4 tickets, and Donatello bought 14 tickets.  If a person randomly selects one raffle ticket from the hat, what is the probability that Raphael purchased the ticket?  Write your answer as a decimal and round three decimal places.

A statistics teacher gives a 10-question multiple-choice pop quiz with five answer choices per problem. Brandon is not prepared and has to guess the answer for each of the 10 questions. The teacher explains that students will receive a free homework pass if they answer at least five questions correctly. What is the probability that Brandon will earn a free homework pass? A. 0.006 B. 0.026 C. 0.033 D. 0.967 E. 0.994

You purchase a brand new car for $17,000 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. X             P(X)