Question

Among 16 electrical components exactly 3 are known not to function properly. If 7 components are randomly selected, find the following probabilities: (i) The probability that all selected components function properly. (ii) The probability that exactly 2 are defective. (iii) The probability that at least 1 component is defective.

Answer 1

Number of ways in which r items can be selected from n, nCr = n!/(r! x (n-r)!)

Number of components that do not function properly = 3

Number of components that function properly = 13

Total number of components = 16

(i) P(all selected components function properly) = 13C7/16C7

= 1,716/11,440

= 0.15

(ii) P(exactly 2 are defective) = P(2 defective and 5 non defective)

= 3C2 x 13C5 / 16C7

= 3 x 1,287 / 11,440

= 0.3375

(iii) P(at least 1 component is defective) = 1 - P(all selected components function properly)

= 1 - 0.15

= 0.85