Question

If 10% of the television pictures tubes burn out before their guarantee period, what is the probability that out of 6 tubes 3 are burnt before guarantee expires.

Answer 1

Let $X=$ the number of the television pictures tubes which are burnt out before their guarantee period: $X\sim Bin(n, p).$

Given $n=6, p=0.1$

$$P(X=3)=\dbinom{6}{3}(0.1)^3(1-0.1)^{6-3}=0.01458$$

The probability that out of 6 tubes 3 are burnt before guarantee expires is

$0.01458.$