Question

Among 7 electrical components, exactly one is known not to function properly. If 4 components are randomly selected, find the probability that all selected components function properly.

a) 1/35
b) 1/21
c) 1/7
d) 1/15

Answer 1

The probability that all selected components function properly is 3/7.

Step-by-step explanation:

To find the probability that all selected components function properly, we need to determine the number of favorable outcomes (components that function properly) and divide it by the total number of possible outcomes. As there are 7 components with only 1 known to be not functional, there are 6 components that function properly. When 4 components are randomly selected, the number of favorable outcomes is the number of ways to select 4 out of the 6 functioning components, which can be calculated using the combination formula: C(6, 4) = 15. The total number of possible outcomes is the number of ways to select any 4 components out of the 7, which can be calculated using the combination formula: C(7, 4) = 35. Therefore, the probability that all selected components function properly is: 15/35 = 3/7.