When a consignment of pens arrives at the retailers ten of t

When a consignment of pens arrives at the retailer\'s, ten of them are tested. The whole batch is returned to the wholesaler if more than one of those selected is found to be faulty. What is the probability that the consignment will be accepted if 2% of the pens are faulty? (Give your answer conventionally rounded to 4 decimal places if needed)

Solution

Answer to the question)
given:

n = 10

Probability of defective = p = 0.02

.

The consignment is rejected if more than 1 are faulty

we want to find the probability of the consignment to be accepted

.

P(x< =1) = P(x=0) + P(x=1)

.

we make use of binomial probability formula to find each of the values of probability

the formula of binomial probability is :

P(X=x) = nCx * p^x * (1-p)^(n-x)

P(x=0) = 10C0 * 0.02^0 * 0.98^10 = 0.8171

P(x=1) = 10c1 * 0.02^1 * 0.98^9 = 0.1667

P(x < =1) = 0.8171 +0.1667

P(x < = 1) = 0.9838