Answer:
a. The number of different combinations of 2 components that can be chosen from a group of 12 is given by the formula:
nC2 = (n!)/(2!(n-2)!), where n is the total number of components
Substituting n = 12, we get:
nC2 = (12!)/(2!(12-2)!) = (12 x 11)/2 = 66
Therefore, there are 66 different combinations of 2 components that can be chosen from the group of 12.
b. The probability that the faulty component will be chosen for testing depends on the number of ways in which the faulty component can be chosen, and the total number of ways in which any 2 components can be chosen.
The probability of choosing the faulty component on the first pick is 1/12, as there is one faulty component out of a total of 12 components.
After the first component has been picked, there will be 11 components left, including one faulty component. Therefore, the probability of picking the faulty component on the second pick, given that the first pick did not pick the faulty component, is 1/11.
Therefore, the probability of picking the faulty component on either the first or second pick is:
P(faulty component) = P(faulty on first pick) + P(faulty on second pick, given not picked on first pick)
P(faulty component) = (1/12) + ((11/12) x (1/11))
P(faulty component) = 1/12 + 1/12
P(faulty component) = 1/6
Therefore, the probability of choosing the faulty component for testing is 1/6 or approximately 0.1667.