Question

Suppose individual components in a system fail with probability 0.04. Find the probability that in a system with 4 components, all components function properly.

A) 0.04
B) 0.16
C) 0.96
D) 0.8464

Answer 1

To calculate the probability that all 4 components in a system function properly with each having a failure rate of 0.04, we use the complement probability 0.96 for each component and multiply them together, resulting in 0.8464.

Step-by-step explanation:

The question involves calculating the probability that all components of a system function properly, given that individual components fail with probability of 0.04. To find the probability that in a system with 4 components all function properly, we need to consider the complementary probability of each component working, which is 1 - 0.04 = 0.96 for one component. Since the functioning of each component is independent of the others, the probabilities can be multiplied together for all four components.

The calculation would then be: 0.96 × 0.96 × 0.96 × 0.96, which is equal to 0.8464. Therefore, the correct answer is D) 0.8464, representing the probability that all four components function properly.