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A mission to Mars depends on the flawless performance of at least 5 out of 7...

A mission to Mars depends on the flawless performance of at least 5 out of 7 boosters. if the probability of all failing at the same time is 0.004, what is the probability that the mission has to abort due to lack of power?

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Answer #1

Let the probability that 1 booster fails is .

The probability that all the boosters fail at the same time is

The mission will fail if 3 or more boosters fail. The number of boosters that fail out of 7 has Binomial distribution with parameters

The PMF is

The probability that the mission has to abort due to lack of power is

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