Question

Multi-part question:

Please show explanation and step by step work.

5. A drag racer has two parachutes, a main and a backup, that are designed to bring the vehicle to a stop after the end of a run. Suppose that the main chute deploys with probability 0.90 and that if the main fails to deploy, the backup deploys with probability 0.90. a. Find the probability that the backup parachute deploys? b. What is the probability that one of the two parachutes deploys?

Answer 1

Let us consider M is main parachute and B is the Backup parachute P(M) is the probability of deploying main parachute is 0.99 and P(B) is the probability of deploying backup parachute which is 0.99.

A) probability that the backup parachute deploy is

P( B∩ M^c) = P(M^c) × P(B|M^c)
= (1 − .99)(. 99) = .0099

B)probability that one of the two
parachutes deploys is given by

P(M∪ B) = P(M) + P(B) − P(M∩ B)
= .99 + .99 − (. 99)(. 99) = .9999