Question

A box contains six 40-watt bulbs, five 60-watt bulbs, and four 75-watt bulbs. If bulbs are selected one-by-one in random order, what is the probability that

1. At least two bulbs must be selected to obtain one that is rated 75 W?
2. [Harder] At least four bulbs will have to be selected to obtain two rated 75 W?

Answer 1

Number of 40-W bulbs = 6

Number of 60-W bulbs = 5

Number of 75-W bulbs = 4

Total number of bulbs = 6 + 5 + 4 = 15

a) P(at least two bulbs must be selected to obtain one that is rated 75 W) = P(first 2 bulbs selected are not 75 W bulbs)

= 11C2/15C2

= 55/105

= 0.5238

b) P(at least four bulbs will have to be selected to obtain two rated 75 W) = P(1 or no 75W bulbs in first three)

= P(one 75 W bulb and two other bulbs) + P(all 3 are not 75W bulbs)

= (4C1 x 11C2 / 15C3) + (11C3 / 15C3)

= (4 x 55 / 455) + (165 / 455)

= 0.8462