Question

A box contains 100 bulbs, 20 of which are defective. 10 bulbs are selected for inspection. Find the probability that: (i) all 10 are defective (ii) all 10 are good (iii) at least one is defective (iv) none is defective Select the correct answer from above options

Answer 1

Given: A box contains 100 bulbs, 20 of which are defective. By using the formula, P (E) = favourable outcomes / total possible outcomes Ten bulbs are drawn at random for inspection, Total possible outcomes are 100C10 n (S) = 100C10 (i) Let E be the event that all ten bulbs are defective n (E) = 20C10 P (E) = n (E) / n (S) = 20C10 / 100C10 (ii) Let E be the event that all ten good bulbs are selected n (E) = 80C10 P (E) = n (E) / n (S) = 80C10 / 100C10 (iii) Let E be the event that at least one bulb is defective E= {1,2,3,4,5,6,7,8,9,10} where 1,2,3,4,5,6,7,8,9,10 are the number of defective bulbs Let E′ be the event that none of the bulb is defective n (E′) = 80C10 P (E′) = n (E′) / n (S) = 80C10 / 100C10 So, P (E) = 1 – P (E′) = 1 – 80C10 / 100C10 (iv) Let E be the event that none of the selected bulb is defective n (E) = 80C10 P (E) = n (E) / n (S) = 80C10 / 100C10