Question

A sample of 10 turbines is selected randomly, without replacement, from your company's stock of 50 turbines. We expect that about 5 of these turbines to have issues of thermal fatigue. What is the probability that, in this sample of 10, 1 or more shows signs of thermal fatigue?

Answer 1

Answer:

The probability that at least 1 turbine shows issues of thermal fatigue is 0.999

Step-by-step explanation:

Let X = number of turbines that have issues of thermal fatigue.

It is provided that 5 of the 50 turbines, in company's stock, have issues of thermal fatigue.

The probability of a turbine having issues of thermal fatigue is:$P(X)=p=\frac{5}{50}=0.10$

A sample of n = 10 turbines are selected.

The random variable X follows a Binomial distribution with parameters n = 10 and p = 0.10.

The probability function of a binomial distribution is:

$P(X=x)={n\choose x}p^{x}(1-p)^{n-x};\ x=0, 1, 2, ...$

Compute the probability that at least 1 turbine shows issues of thermal fatigue as follows:

P (X ≥ 1) = 1 - P (X < 1)

             = 1 - P (X = 0)

             $=1-{10\choose 0}(0.10)^{0}(1-0.10)^{10-0}\\=1-(1\times1\times0.0000000001)\\=0.999$

Thus, the probability that at least 1 turbine shows issues of thermal fatigue is 0.999.