Question

An airplane is built to be able to fly on one engine. If the plane' s four engines operate independently, and each has a 1% chance of failing in any given four-hour flight, what is the chance the plane will fail to complete a four-hour flight to its destination due to engine failure?

Answer 1

An airplane or aeroplane (informally plane) is a powered, fixed-wing aircraft that is propelled forward by thrust from a jet engine, propeller or rocket engine. Airplanes come in a variety of sizes, shapes, and wing configurations.

Airplane (disambiguation)

Answer 2

Answer:

Probability that the plane will fail to complete a four-hour flight to its destination due to engine failure = 0.00000001

Explanation:

Let's say, P(f) is the probability of an engine failure: P(f)=$\frac{1}{100} =0.01$

Plane will fail to complete four-hour flight only if all four of its engine fails.

Here, failing of either of the four engine does not depend on failure of any other engine. This means failure of an engine is an independent event.

Probability of all 4 engine failing mid flight = P(f $\bigcap$ f $\bigcap$ f $\bigcap$ f)

P(f $\bigcap$ f $\bigcap$ f $\bigcap$ f) = P(f)*P(f)*P(f)*P(f) = $\frac{1}{100}*\frac{1}{100} *\frac{1}{100} *\frac{1}{100} =\frac{1}{10^8}=0.00000001$

The probability that the plane will fail to complete a four-hour flight to its destination due to engine failure is one in a hundred million.

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