Question

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 are 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

Answer 1

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

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