Answer:
P = αP(x≥k,p1) + (1-α)P(x≥k,p2)
Step-by-step explanation:
The probability that k of n components function on a day follows a binomial distribution, so the probability is:
Where p is the probability that a component function and nCk is
So, the probability that at least k of the n components function on a day is:
P(x≥k,p) = P(k,p) + P(k+1,p) + P(k+2,p) + ... + P(n,p)
Then, if it is rain, the probability of the function p is equal to p1, if it isn't the probability p is equal to p2, so the probability P that the satellite system will function is:
P = αP(x≥k,p1) + (1-α)P(x≥k,p2)
Where, P(x≥k,p1) and P(x≥k,p2) are equal to:
P(x≥k,p1) = P(k,p1) + P(k+1,p1) + P(k+2,p1) + ... + P(n,p1)
P(x≥k,p2) = P(k,p2) + P(k+1,p2) + P(k+2,p2) + ... + P(n,p2)