An aircraft is equipped with three engines that operate independently. The probability of an engine failure is .01. What is the probability of a successful flight if only one engine is needed for the successful operation of the aircraft?
To find the probability of a successful flight when only one engine is needed, we need to consider the probability of all three engines not failing.
The probability of an engine failure is given as 0.01. Therefore, the probability of one engine not failing is 1 minus the probability of failure, which is 1 - 0.01 = 0.99.
Since the engines operate independently, the probability of all three engines not failing is obtained by multiplying the probability of not failing for each engine.
So, to find the probability of a successful flight with one engine, we multiply the probability of one engine not failing (0.99) by itself three times, since there are three engines:
0.99 * 0.99 * 0.99 = 0.9703.
Therefore, the probability of a successful flight with only one engine needed is approximately 0.9703 or 97.03%.
To summarize, the probability of a successful flight if only one engine is needed can be found by multiplying the probability of each engine not failing. In this case, the probability is 0.99 raised to the power of 3.