Answer to Question #109784 in Statistics and Probability for Gabriel Burns

Question

Two sirens are installed in a factory. The probability that the first one will work is 0.90, and the probability that the second one will work is 0.85. What is the probability that at least one will NOT work?

Answer 1

First Solution

Let's imagine opposite situation: both of sirens will work.

The probability of such situation is 0.90*0.85=0.765

So, the probability that at least one will not work is 1-0.765=0.235.

Second Solution

Let's calculate probability of each situation where at least one will not work.

First will work and second won't: 0.9*(1-0.85)=0.135

First won't work and second will work: (1-0.9)*0.85=0.085

Both won't work: (1-0.9)(1-0.85)=0.015

Sum of all 3 gives us: 0.135+0.085+0.015=0.235.

Answer: 0.235