Answer to Question #130694 in Statistics and Probability for Zain Asim

Question

4 items are taken at random from a box of 12 items and inspected. The box is rejected if more than 3 item is found to be faulty. If there are 5 faulty items in the box .Find the probability that the box is rejected.

Answer 1

Let success be defined as selecting a defective item from the box.

Given that there are 5 defective items in a box of 12 items,

The probability of success p = 5/12 = 0.41666

Probability of failure q = 7/12 = 0.58333

Since we are sampling only 4 items out of 12 items n = 4

Thus probability that the box getting rejected is only when all the 4 items (4 out of 4) on a random selection from the box are found to be defective.

Hence we can find the probability P(x) using the binomial distribution formula,

P(x) = $\frac {n!}{(n-x)!*x!}$*p^x*q^n-x

P(x) = P(4) = 0.03014

Above is the probability that the box will be rejected.