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During World War II, the British found that the probability that a bomber is lost through enemy action on a mission over occupied Europe was 0.05 Assuming that missions are independent, find the probability that a bomber returned safely from 20 missions.

Short Answer

Expert verified

The probability is 0.3585

Step by step solution

01

Step 1. Given Information

The chance of the bomber being lost is 0.05 The missions are self- contained.

02

Step 2. Concept Used

Two mutually exclusive events can never be independent since if one happens, the other is nearly surely going to happen as well.

03

Step 3. Calculation

The bomber's safety is calculated as follows:P(Safe)=1-P(lost)P(Safe)=1-0.05=0.95

After 20trips, the probability that the bomber will return safely is computed as follows:P(Willcomebacksafely)=0.9520=0.3585

As a result, the necessary probability is 0.3585

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