A box contains six 40W bulbs five 60W bulbs and nine 75W bul

A box contains six 40-W bulbs, five 60-W bulbs, and nine 75-W bulbs. If bulbs are selected one by one in random order, what is the probability that at least two bulbs must be selected to obtain one that is rated 75 W? (Round your answer to three decimal places.)

Solution

Let X be the number of bulbs that must be selected to obtain one that is rated 75 W

P(X>=2) = 1 - P(X<2) = 1 - P(X=1)

where, P(X=1) is the probability of getting 75W in the 1st selection

P(X=1) = 9/20 = 0.450

So, P(X>=2) = 1 - 0.450 = 0.550