A box in a supply room contains 24 compact luorescent lightbulbs, of which are r
ID: 3302321 • Letter: A
Question
A box in a supply room contains 24 compact luorescent lightbulbs, of which are rated 13-watt, 9 are rated 13 watt, and 7 are rated 23 watt. Suppose that three of these bulbs are randomly selected. (Round your answers to three decimal places.) (a) What is the prohability that exactly two of the salected hulhs ara rated 23-watt? (b) What is the probability that all three ot the bulbs have the same rating? 10.0865 () What is the probability that bulb of each type is selected? (d) If bulbs are selected one by one until a 23-watt bulb is obtalned, what is the probability that it is necessary to examine at least 6 bulbs? 0 0919 Need Help? Peaad Submit Answr Save ProgressPractice Another VerslonExplanation / Answer
(a) The two 23-watt bulbs can come in 7C2 = 21 ways.
The remaining bulb can come in 17 ways.
Total ways of selecting 3 bulbs = 24C3 = 2024
=> Probability = 21 * 17 / 2024 = 0.176.
(b) If all three bulbs are 13-watt, this can be done in 8C3 ways.
If all three bulbs are 18-watt, this can be done in 9C3 ways.
If all three bulbs are 23-watt, this can be done in 7C3 ways.
Total number of ways of selecting three bulbs with same rating
= 8C3 + 9C3 + 7C3
= 56 + 84 + 35
= 175
Probability = 175 / 2024 = 0.086
(Note: The question asks THREE decimal places)
(c) The three types of bulbs can come in 8,9 and 7 ways.
Total number of ways = 8*9*7 = 504
Probability = 504 / 2024 = 0.249
(d) Probability of 23-watt bulb = 7/24
=> Probability that a bulb chosen is not 23-watt bulb = 1 - 7/24 = 17/24
=> Probability that the first five bulbs are not 23-watt bulbs = (17/24)5
= 0.178
Thus the probability that it is necessary to examine atleast 6 bulbs
= 0.178
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