# Question: Following the loss of the Challenger space shuttle a study

Following the loss of the Challenger space shuttle, a study was done to fnd better ways to measure and control for risk. One way to reduce the risk of failure is to have redundant (backup) systems. Suppose you have designed a component for the new Mars explorer that, during pre fight tests, malfunctioned 10% of the time. You’ve decided to install an identical unit (that is, one with a 10% failure rate) as a backup. Based on tests for the two components together, you have found that, overall, both the components failed simultaneously about 6% of the time.

a. What is the probability that at least one of the components will function properly?

b. What is the probability that the backup component will fail given that the primary component fails?

c. Is the performance of one component statistically independent of the performance of the other? Explain.

a. What is the probability that at least one of the components will function properly?

b. What is the probability that the backup component will fail given that the primary component fails?

c. Is the performance of one component statistically independent of the performance of the other? Explain.

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