Question

A drag racer has two parachutes, a main and a backup, that are designed to bring the vehicle to a stop (combined with the brakes) after the end of a run. Suppose that the main chute deploys with probability 0 . 95, and that if the main fails to deploy, the backup deploys with probability 0.999.

Required:
a. What is the probability that one of the two parachutes deploys?
b. What is the probability that the backup parachutes deploys?

Answer 1

a. 0.99995 = 99.995% probability that one of the two parachutes deploys

b.0.04995 = 4.995% probability that the backup parachutes deploys

Explanation:

a. What is the probability that one of the two parachutes deploys?

Either the first deploys(with probability 95%), or the first does not deploy(probability 5%) and the second does(probability 99.9%). So

`p = 0.95 + 0.05*0.999 = 0.99995`

0.99995 = 99.995% probability that one of the two parachutes deploys

b. What is the probability that the backup parachutes deploys?

The first does not deploy(probability 5%) and the second does(probability 99.9%). So

`p = 0.05*0.999 = 0.04995`

0.04995 = 4.995% probability that the backup parachutes deploys