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Alex787 [66]
3 years ago
7

5. A box in a supply room contains 15 compact fluorescent lightbulbs, of which 5 are rated 13-watt, 6 are rated 18-watt, and 4 a

re rated 23-watt. Suppose that three of these bulbs are randomly selected. a. What is the probability that exactly two of the selected bulbs are rated 23-watt
Mathematics
1 answer:
skelet666 [1.2K]3 years ago
3 0

Answer:

176/1125 or 0.156

Step-by-step explanation:

There are 15 bulbs, of which 4 are 23-watt. The probability of selecting a 23-watt bulb = 4/15. If we call this probability x, then x = 4/15.

The probability of selecting a 13-watt or 18-watt bulb is the probability of not selecting a 23-watt bulb. If we call this y, y = (6+5)/15 = 11/15. It follows that x and y are mutually exclusive. Here, we have a binomial distribution.

The number of ways of selecting exactly two 23-watt bulbs out of three is

\binom{3}{2} = 3

The probability of selecting them is

3x^2y = 3\times\left(\dfrac{4}{15}\right)^2\times\dfrac{11}{15}=\dfrac{176}{1125}= 0.156

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