Probability Question The required probability that a twostag

Probability Question:

The required probability that a two-stage rocket will perform successfully is 0.97. The reliability for the first stage is 0.99. The reliabilities for the two stages are independent. Determine the reliability for the second stage.

Solution

Let it be x, since these are in series, P(system works) = P(both stage wors) = P(first works) * P(second works)

0.97 = 0.99 * x

=> x = 0.97979797979797979798

Thus, reliability of second stage is ~ 0.9798