Question

An assembly of four components works if at least one of its four components works (components in parallel). If each component has a reliability of 0.97 and the components operate independently, what is the probability that the assembly works

Answer 1

0.89

Explanation:

Question says components have reliability of 0.97 and each component works independently.

We are required to calculate probability that the assembly works

We solve this using the binomial distribution

P(X=4)

4C4(0.97)⁴(1-0.97)^4-4

4C4 = 1

0.97⁴ = 0.8859281

1-0.97^4-4 = (0.03)⁰ = 1

Multiply all values

1 x 0.88529281 x 1

= 0.88529281

When approximated, we get 0.89

In conclusion the probability that the assembly works is 0.89

Thank you!