Project: Shuttle

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When the space shuttle Challenger exploded shortly after lift off, it was the responsibility of the investigation team to find the cause of this tragedy. Their findings assigned the cause of the explosion to the "O-rings" whose function was to contain the rocket fuel within the fuel cells.

When the rocket fuel leaked outside the fuel cell, it was ignited by the exhaust and the subsequent explosion followed. The space shuttle had two sets of O-rings. They were assumed to act independently. However, further study proved them to be dependent.

Before the next space shuttle was launched, a third set of O-rings was installed. This new O-ring is truly independent of the other two.

There were two statements made during the analysis of the space shuttle disaster that can be proved using statistics.

Statement #1: "When the space shuttle was launched, the crew had the same chances of surviving as if they were playing Russian Roulette using a gun having 8 chambers and 1 bullet."

Compare Russian Roulette to the launch of the space shuttle.
Russian Roulette involves putting one bullet into a gun having 8 chambers, spinning the chambers, putting the gun to your head and pulling the trigger.
A. Calculate for Russian Roulette:
1. P(Surviving Russian Roulette)

B. Launching of the Space Shuttle
     The O-ring (gasket) keeping the fuel gases from escaping is held in place by 6 field joints.
     The P(A single field joint functioning) = 0.977. The 6 field joints act independently of
     each other and all six field joints must function properly to prevent an explosion on lift-off.
     Calculate:
     1. P(O-ring functioning) which means a safe lift-off.

Statement #2: "When the space shuttle was redesigned, it had an additional O-ring installed that was truly independent of the other two O-rings. This new O-ring increased the probability of the O-rings functioning successfully."

A. Using the same O-ring probabilities from the previous problem, fill in the probability
    distribution table for the O-rings. The initial set of two rings are dependent and act
     as one O-ring (when one O-ring moved, so did the other O-ring.) The newly installed
     third O-ring is truly independent of the other O-rings. Treat the third O-ring as a
     second O-ring.

Event	Probability
First set of O-rings function and second O-ring functions
First set of O-rings malfunction and second O-ring functions
First set of O-rings function and second O-ring malfunctions
First set of O-rings malfunction and second O-ring malfunctions

B. Let x represent the number of O-ring malfunctions. Use the probabilities from the above
table to fill in the probability distribution table.

C. Use the probability distribution table above to find:
1. P(Explosion on lift-off)

x	P(x)
0
1
2