Question

Question 11 (1 point) The probability that a certain make of car will need repairs in the first six months is 0.33. A dealer sells 4 such cars. What is the probability that at least one of them will require repairs in the first six months? Write only a number as your answer. Round your answer to four decimal places (for example: 0.7319). Do not write as a percentage. Your Answer: Answer

Answer 1

Let X = number of cars need repairs in the first six months.

here n = 4, and p = 0.33

So we can use binomial distribution to find the probability of the given event.

Here we want to find probability of at least one of the car out of 4 cars need repairs in the first six months.

Mathematically, P(X >= 1 ) = 1 - P( X < 1 ) = 1 - P( X = 0) ....( 1 )

Let P(X = 0) = P( None of the four cars need repairs in the first six months.) = (1- 0.33)^4 = 0.67^4 = 0.2015

Plug this value in equation ( 1 ), we get .

P(X >= 1 ) = 1 - 0.2015 = 0.7985 ( This is the final answer).