Question

A starter motor used in a space vehicle has a high rate of reliability and was reputed to start on any given occasion with probability .99999. What is the probability of at least one failure in the next 10,000 starts?

Answer 1

Answer:

0.095163

Step-by-step explanation:

given that a starter motor used in a space vehicle has a high rate of reliability and was reputed to start on any given occasion with probability .99999

Here we find that for any start, there are exactly two outcomes either success or failure.

Also each start is independent of the other since p = 0.99999 for succss is given constant.

Thus X no of successes is binomial with p = 0.99999 and n =10000

If Y is taken as failure then Y is binomial with p' = 0.00001 and n =10000

Required probability

= the probability of at least one failure in the next 10,000 starts

= 1-P(no failure in 10000 starts)

=$1-(0.99999)^{10000} \\=0.095163$