Question: The January 1986 mission of the Space Shuttle Challenger was the 25^th such shuttle mission. It was unsuccessful due to an explosion caused by an O-ring seal failure.

a) According to NASA, the probability of such a failure in a single mission was 1/60000. Using this value of p and assuming all missions are independent, calculate the probability of no mission failures in 25 attempts.

b) In another report, it only states that such a failure occurs at one in 60,000 missions (of course we haven’t seen this many missions yet). Assuming all missions are independent, calculate the probability of no mission failures in 25 missions.

c) According to a study conducted for the Air Force, the probability of such a failure in a single mission is 1/35. Recalculate the probability of no mission failures in 25 mission attempts.

d) How small must the probability p be made in order to ensure that the probability of no mission failures in 25 attempts is 0.999?