the probability that a key component of a stand -by generator will fail during a power outage is q. A generator works if at least half of its key component work.Assuming that the the generator has four key components. find the probability that the generator will work

Answer 1

All of the parts have to work.
probability of part failing =q
probability of part working = (1-q)
4 parts, binomial distribution
4Ck = 4!/[k!(4-k)!]
4C4 = 1 , 4C3= 4 , 4C2= 6

P4 of 4 working = 1 (1-q)^4 q^0= (1-q)^4
P3 of 3 working = 4 (1-q)^3 q^1
P2 of 2 working = 6 (1-q)^2 2^2
add those