Question

A box in a certain supply room contains four 40-W lightbulbs, five 60-W bulbs, and six 75-W bulbs. Suppose that three bulbs are randomly selected. What is the probability that exactly three of the selected bulbs are rated 75-W? (15 points)

Answer 1

Answer:

Probability that exactly three of the selected bulbs are rated 75-W is 0.044.

Step-by-step explanation:

We are given that a box in a certain supply room contains four 40-W light bulbs, five 60-W bulbs, and six 75-W bulbs.

And we have to find the probability that exactly three of the selected bulbs are rated 75-W.

Here, we will use Combinations for selection procedure, i.e.;

                    $^{n} C_r = \frac{n!}{r! \times (n-r) !}$

So, number of ways of selecting three 75-W rated bulbs from total of six 75-W rated bulbs in a box is given by = $^{6} C_3$

Total number of ways of selecting three bulbs from total of 15 bulbs (4 + 5 + 6) in a box = $^{15} C_3$

Therefore, probability that exactly three of the selected bulbs are rated 75-W is given as = $\frac{^{6} C_3}{^{15} C_3}$ = $\frac{\frac{6!}{3! \times 3!} }{\frac{15!}{3! \times 12!} }$

                             = $\frac{6!}{3!} \times \frac{12!}{15!}$ = $120 \times \frac{1}{2730}$ = $\frac{4}{91}$

                             = 0.044

Hence, the required probability is 0.044.