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grandymaker [24]
3 years ago
10

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)
Mathematics
1 answer:
GarryVolchara [31]3 years ago
3 0

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.

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