Answer to Question #188498 in Statistics and Probability for LE5

Question

Rey works in a semiconductor company where he is tasked to manage semiconductor fabrication. He deduced that for every 100 semiconductors, 5 of which are defective. After considering all scenarios, he made the necessary steps to improve the process.

During a site visit, what would be the probability that none of them are defective if the checker selects 3 semiconductors to be tested?

Answer in percentage form and use four decimal places

Answer 1

Probability of defective semiconductors-

$p=\dfrac{5}{100}=0.05$

then $q=1-p=1-0.05=0.95$

n=3,

Let X be the random variable and denote the number of defective semiconductor

Probability that none of the semiconductor is defective-

$P(X=0)=^nC_0p^0q^{n-0}$

$=^3C_0(0.05)^0(0.95)^3\\ =0.8573$