Question

2. A two-stage rocket is in development. The required probability is for the overall rocket to be a minimum of 97% reliable for a successful mission. The first stage is a previously developed design with a known reliability of 99%. The reliability measures for the two stages are independent. What must the minimum reliability for the second stage be

Answer 1

Answer: The minimum reliability for the second stage be 0.979.

Step-by-step explanation:

Since we have given that

Probability for the overall rocket reliable for a successful mission = 97%

Probability for the first stage = 99%

We need to find the minimum reliability for the second stage :

So, it becomes:

P(overall reliability) = P(first stage ) × P(second stage)

$0.97=0.99\times x\\\\\dfrac{0.97}{0.99}=x\\\\0.979=x$

Hence, the minimum reliability for the second stage be 0.979.