Question

Successful implementation of a new system is based on three independent modules. Module 1 works properly with probability 0.96. For modules 2 and 3, these probabilities equal 0.95 and 0.90. Compute the probability that at least one of these three modules fails to work properly.

Answer 1

Answer: There is a probability that at least one of these three modules fails to work properly is 0.18.

Step-by-step explanation:

Since we have given that

Probability of Module 1 works properly = 0.96

Probability of Module 2 works properly = 0.95

Probability of Module 3 works properly = 0.90

We need to find the probability that at least one of these three modules fails to work properly.

First we will find the probability that none of them fails to work properly.

So, Probability that none of them fails to work properly is given by

$0.96\times 0.95\times 0.90\\\\=0.8208$

So, Probability that at least one of these three modules fails to work properly is given by

$1-P(\text{none of them fails to work properly})\\\\=1-0.8208\\\\=0.1792\\\\=0.18\ approx.$

Hence, there is a probability that at least one of these three modules fails to work properly is 0.18.