find exactly 2 of the next 8 components tested survive

Question

the probability that a certain kind of component will survive a shock test is 0.7 then

Answer 1

Binomial expansion applies: (p+(1-p))^8=1 represents the sum of all individual probabilities.

This is (1-p)^8+8p(1-p)^7+28p^2(1-p)^6+... The first term is the probability of no survivors; the second term the probability of one survivor; the third the probability of two survivors=28*0.7^2*0.3^6=0.01 or 1%.