A plane's engines start successfully at a given attempt with a probability of 0.75. Any time that the mechanics are unsuccessful in starting the engines, they must wait five minutes before trying again. Find probability that the plane is launched within 10 minutes.

The probability is 0.984

Step-by-step explanation:

From the given data there will be 3 tries. at 0 minutes, 5 minutes and 10 minutes

Probability of successful start is 0.75, this means probability of failed start will be 1-0.75 = 0.25

In the first attempt at 0 minute, the probability is 0.75

At 5 minute which is second trial, probability is (0.75) (0.25)

At 10 minute, which is third trial, probability is (0.75) (0.25) (0.25)

mathematically the probability of starting the engine in 10 minutes = (1 - probability of not starting the engine in 10 minutes)

This means the probability of failure in the third attempt would be (1-0.75) ^3 = 0.25^3

The probability that the engine will launch in 10 minutes is thus;

1 - 0.25^3 = 0.984