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# A box in a supply room contains 15 compact fluorescent ISBN: 9780321629111 32

## Solution for problem 39E Chapter 2

Probability and Statistics for Engineers and the Scientists | 9th Edition

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Problem 39E

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? b. What is the probability that all three of the bulbs have the same rating? c. What is the probability that one bulb of each type is selected? d. If bulbs are selected one by one until a 23-watt bulb is obtained, what is the probability that it is necessary to examine at least 6 bulbs?

Step-by-Step Solution:

Answer : Step 1 : Given a box in a supply room contains 15 compact fluorescent light bulbs, 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). There is a total of 5 + 6 + 4 = 15 bulbs. Three of these bulbs are randomly selected. So15c 3 Then (4c )2(11c )1 (2 of the four 25-watt bulbs, 1 of the remaining 11 bulbs). Now we have to find the probability that exactly two of the selected bulbs are rated 23-watt. (4c ) (11c ) P (two are 25-W) = 2 1 (15c 3 (6) (11) P (two are 25-W) = (455) (66) P (two are 25-W) = (455) P (two are 25-W) = 0.145 Therefore the probability that exactly two of the selected bulbs are rated 23-watt is 0.145. Step 2 : b). Let the probability that all three of the bulbs have the same rating. Break into three cases: 3 of one type of bulb : (5c3) (6c 3 (4c 3 P(all three of the bulbs ) = (15c ) 3 (10) + (20) + (4) P(all three of the bulbs ) = (455) (34) P(all three of the bulbs ) = (455) P(all three of the bulbs ) = 0.0747

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##### ISBN: 9780321629111

Probability and Statistics for Engineers and the Scientists was written by and is associated to the ISBN: 9780321629111. The full step-by-step solution to problem: 39E from chapter: 2 was answered by , our top Statistics solution expert on 05/06/17, 06:21PM. The answer to “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? b. What is the probability that all three of the bulbs have the same rating? c. What is the probability that one bulb of each type is selected? d. If bulbs are selected one by one until a 23-watt bulb is obtained, what is the probability that it is necessary to examine at least 6 bulbs?” is broken down into a number of easy to follow steps, and 106 words. This textbook survival guide was created for the textbook: Probability and Statistics for Engineers and the Scientists, edition: 9. Since the solution to 39E from 2 chapter was answered, more than 1056 students have viewed the full step-by-step answer. This full solution covers the following key subjects: watt, bulbs, selected, Probability, rated. This expansive textbook survival guide covers 18 chapters, and 1582 solutions.

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