This question is based on stats and probability.

The question is below:

I have included certain values I believe are needed to answer this question. (at a 98% the corresponding (alpha) value is 0.02 and (Z/2) is 2.326).

A manned space launch system has an overall reliabilityof98%, or one "failure" in 50 launches. There are three categoriesoffailure, i.e., those that lead to in-flight destructionofthe vehicle, those that lead to a safe return-to-launch-site or downrange abort, and those that lead to an abort to a stable but degraded orbit allowing primary mission completion. These failures occur with refutive probabilities of 5, 75, and 20%.Ofthe abort-to-orbit cases, 40% allow the primary mission to be completed, while 60% lead to lossofmission becauseofthe degraded orbit.

1. What is the overall probabilityoflossofmission for a given launch?

(a) Given that a failure occurs, what is the probabilityofprimary mission completion?

(b) Given that the vehicle reached orbit, what is the probability that an abort-to-orbit occured?

(c) Given that lossofmission has occurred, what is the probabilityofcrew survival?