Question

Among 14 electrical components exactly 3 are known not to function properly. If 6 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

Total 14 electrical components .....

3 components are known not to function properly.

Therefore, 14-3 = 11 components are known to function properly.

choosing 6 components are randomly selected ..........

Therefore, sample space: 14C6

(i) P(all 6 function) = 11C6 / 14C6

Therefore, 11C6 = 14C6 = 462 = 3003 = 0.15

i.e. probability of Zero defective is 0.15

ii)

P( 2 defective) = (3C2 * 11C4 ) / 14C6 = 0.33

iii) P(at least one component is defective) = 1 - P (0 defective)

earlier we find that in part (i), P(0 defective) = 0.15

Therefore

P(at least one component is defective) = 1 - 0.15 = 0.85