Laura and Philip each fire one shot at a target. Laura has probability 0.5 of hitting the target, and Philip has probability 0.3. The shots are independent. a) Find the probability that the target is hit. b) Find the probability that the target is hit by exactly one shot. c) Given that the target was hit by exactly one shot, find the probability that Laura hit the target.

Jack has just been given a ten-question multiple choice quiz in history class. Each question has five answers, of which only one is correct. Since Jack has not attended class recently, he does not know any of the answers. Assuming Jack guesses randomly on all ten questions, find the probability that he will answer six or more of the questions correctly and avoid an F.

A prize is placed at random in one of three boxes. You pick a box (and do not open it). Now, the dealer (who knows where the prize is) chooses one of the other two boxes, opens it and shows you that it is empty. She then gives you the opportunity to keep your original box or switch to the other unopened box. Find the probability of winning the prize if you switch. Find the probability of winning the prize if you stay. Should you stay or switch?

Give the probability in decimal form (correct to two decimal places). A calculator may be helpful with this problem.The campus vets club is having a raffle and is selling 1,500 tickets. If the people on your floor of the dorm bought 255 of those tickets, what is the probability that someone on your floor will hold the winning ticket?

Help with questions A-E please