Question

Suppose that the probability of “catastrophic failure” for solid rocket motors is 2/50. Assuming rocket failures are statistically independent, determine the probability that for two solid rocket motors, at least one will fail.

Answer 1

The probability of a catastrophic failure = 2/50

==>p(C) = 2/50

Let us assume that the two solid motors are A and B

Therefore, failure of A p(A) = 2/50 and failure of B p(B) = 2/50

For statistically independent events probability of occurring both the events = probability of occurrence of event 1 * probability of occurrence of event 2

Therefore, p(A and B) =p(A) * p(B)

Now, the question is asking us to calculate p(A or B) = p(A) + p(B) - p(A and B)

p(A or B) =2/50+2/50 - (2/50)*(2/50) = 0.0784