Answer:
The answers to the questions are as follows
a) k = 0, P = 0.3
k = 1, P = 0.5
k = 0, P = 0.2
b) The probability that enough power will be available is 0.5.
Explanation:
To solve the question we write the parameters as follows
Probability that the first power source works = P(A) = 0.4
Probability that the second power source works = P(B) = 0.5
When both sources are supplying power we have the probability = 1
If non of them is producing the probability = 0
a) The probability that exactly k sources work for k=0,1,2 is given by
For k = 0, probability = (1- P(A))× (1- P(B)) = 0.6 × 0.5 =0.3
Therefore the probabilities that exactly 0 source work = 0.3
for k = 1 we have the probability = P(A)(1-P(B)) + P(B)(1-P(A)
= 0.4(1-0.5)+0.5(1-0.4) = 0.2 + 0.3 = 0.5
The probabilities that exactly 1 source work = 0.5
for k = 2 we have the probability given by = P(A) × P(B) = 0.4 × 0.5 = 0.2
Therefore the probability that exactly 2 sources work = 0.2
b) The probability that enough power will be available is
0 × P(k = 0) + 0.6 × P(k = 1) + 1 × P(k = 2)
0 × 0.2 + 0.6 × 0.5 + 1 × 0.2 = 0.5
The probability that enough power will be available is 0.5.
