A manufacturer knows that 14% of the products it produces are defective. Find the probability that among 7 randomly selected products, at least one of them is defective.

Question

asked Mar 27, 2021 164k views

1 Answer

Jeffalstott · Answer 1 · 2021-04-01T20:28:21+0000

Answer: 0.6521

Explanation:

According to the Binomial distribution , the provability of getting x successes in n trials is given by :-

P(x)=^nC_xp^x(1-p)^(n-x) , where p=probability of getting success in each trial.

Let x denotes the number of defective products.

here , n=7 and p =0.14

Then, the probability that among 7 randomly selected products, at least one of them is defective= P(X ≥ 1) =1- P(X<1)

= 1- P(X=0)

=1-^7C_0(0.14)^0(1-0.14)^7

$=1-(1(1)(0.86)^7\ \[\because ^nC_0=1]$

=1-0.347927822217

$=0.652072177783\approx0.6521$

Hence, the probability that among 7 randomly selected products, at least one of them is defective is 0.6521 .