Question

A starter motor utilized in a space vehicle possesses high reliability and is reputed to start on any given occasion with probability 0.99999.

(a) (4 points) What is the probability of at least one failure to start in the next 10,000 attempts?

(b) (2 points) What is the approximate distribution for the number of failures to start, in 10,000 attempts? Indicate the parameters of this distribution.

(c) (2 points) If there is another starter motor with the same characteristics and that operates independently of the first starter motor, what is the approximate probability that both starters fail to start at least once on their next 10,000 attempts?

Answer 1

(a) Probability = $1 - \binom{10000}{0}(0.00001)^0*(0.99999)^{10000} = 0.0952$

(b) The distribution is binomial.

Mean = 10000*0.00001 = 0.1

Standard deviation = $\sqrt{}$ 10000*0.00001*0.99999 = 0.316

(c) Probability = 0.0952*0.0952 = 0.0091