According to NASA, each space shuttle in the U.S. fleet has 1,500 “critical items” that could lead to catastrophic failure if rendered inoperable during flight. NASA estimates that the chance of at least one critical-item failure within the shuttle’s main engines is about 1 in 60 for each mission. To build space station Freedom, suppose NASA plans to fly 8 shuttle missions a year for the next decade.
a. Find the probability that at least 1 of the 8 shuttle flights scheduled next year results in a critical-item failure.
b. Find the probability that at least 1 of the 40 shuttle missions scheduled over the next 5 years results in a critical-item failure.