Question

Among 7 electrical components exactly one is known not to function properly. If 2 components are randomly selected, find the probability that all selected components function properly.

a) 0.2857
b) 0.8571
c) 0.5714
d) 0.6297
e) 0.7143
f) None of the above

Answer 1

To find the probability that both selected components are functioning, combinatorics is used to determine the total number of selections and the number of functioning selections, resulting in the correct answer of e) 0.7143.

Step-by-step explanation:

The question asks to find the probability that two randomly selected electrical components from a set of seven, which contains exactly one non-functioning component, both function properly. To solve, we use combinatorics.

The total number of ways to select 2 components out of 7 is given by the combination formula: C(n, k) = n! / (k!(n-k)!), where n is the total number of components and k is the number of components we want to choose. In this case, n=7 and k=2. So we have C(7, 2) = 7! / (2!(7-2)!) = 21.

Since there is one non-functioning component, there are 6 functioning components. The number of ways to choose 2 functioning components is C(6, 2) = 6! / (2!(6-2)!) = 15.

Thus, the probability that both selected components are functioning is the ratio of the number of ways to select 2 functioning components to the total number of ways to select any 2 components: 15/21 = 0.7143.

The correct answer corresponds to option e) 0.7143.