The January 1986 mission of the Space Shuttle Challenger was the 25th 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 1/60,000. Using this value of p and assuming all missions are independent, calculate the probability of no mission failures in 25 attempts. Then calculate the probability of at least one mission failure in 25 attempts. . b According to a study conducted for the Air Force, the probability of such a failure in a single mission was 135. Recalculate the probability of no mission failures in 25 attempts and the probability of at least one mission failure in 25 attempts. c Based on your answers to parts a and b, which value of p seems more likely to be true? Explain. d How small must p be made in order to ensure that the probability of no mission failures in 25 attempts is .999