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

To find the probability of two 23-watt bulbs being selected, calculate the number of possible combinations of bulbs. Then calculate the probability of selecting two 23-watt bulbs and one non-23-watt bulb. Finally, simplify and calculate the probability.

Step-by-step explanation:

To find the probability that exactly two of the selected bulbs are rated 23-watt, we need to calculate the probability of selecting two 23-watt bulbs and one non-23-watt bulb from the box. The total number of ways to select three bulbs from 15 is given by the combination formula C(15, 3) = 455.

The number of ways to select two 23-watt bulbs from the 4 available is given by the combination formula C(4, 2) = 6. The number of ways to select one non-23-watt bulb from the remaining 11 available is given by the combination formula C(11, 1) = 11.

Therefore, the probability of exactly two 23-watt bulbs being selected is 6/455 *11/455, which simplifies to 66/20995 or approximately 0.00314.