Question

A lot of 100 watches is known to have 10 defective watches. If 8 watches are selected (one by one with replacement) at random, what is the probability that there will be at least one defective watch?

Answer 1

Probability of defective watch out of 100 watches = `10/100 = 1/10`.

Here, n = 8

p = `1/10`

q = `1 - 1/10 = 9/10`

And r ≥ 1

P(X ≥ 1) = 1 – P(x = 0)

= `1 - ""^8"C"_0 (1/10)^0 (9/10)^(8 - 0)`

= `1 - (9/10)^8`

Hence, the required probability is `1 - (9/10)^8`.