Question

Sixty-eight percent of all vehicles at a certain emissions inspection pass the inspection. Assuming that successive vehicles pass or fail independently of one another. Calculate the following probabilities:

1. At least one of the next 11 vehicles inspected fail.
2. Exactly five of the next 11 vehicles inspected passes.
3. Given that more than three of the next 11 vehicles inspected fails, what is the probability that no more than eight of the next 11 vehicles inspected fails?

Answer 1

Hello Sir/ Mam

Let X be the number of vehicles that pass the inspection.

Hence, X is binomially distributed with p = 68% and n = 11.

(a) The required probability = 98.56%

(b) The required probability = 7.21%

(c) The required probability = %

I hope this solves your doubt.

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