Question

Among 8 electrical components exactly one is known not to function properly. If 3 components are randomly selected, find the probability that at least one does not function properly.

Answer 1

The probability that at least one component does not function properly when selecting 3 components out of 8 can be found by subtracting the probability that all components function properly from 1. The probability that a component does not function properly is 7/8. Therefore, the probability that at least one component does not function properly is 169/512.

Step-by-step explanation:

The probability that at least one component does not function properly can be found by subtracting the probability that all 3 components function properly from 1.

To find the probability that a component does not function properly, we can use the fact that exactly 1 component is known to be defective out of the 8 components.

So, the probability that a component does not function properly is 1 minus the probability that a component functions properly, which is 1 - 1/8 = 7/8. Therefore, the probability that at least one component does not function properly when selecting 3 components is:

P(at least one component does not function properly) = 1 - P(all components function properly)

P(at least one component does not function properly) = 1 - (7/8)^3 = 1 - 343/512 = 169/512.