I am having trouble with this homework question A box in a supply room contains 24 compact fluorescent lightbulbs, of which 8 are rated 13-watt, 9 are rated 18-watt, and 7 are rated 23-watt. Suppose that three of these bulbs are randomly selected. (Round youranswers to three decimal places.)(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?

Answered: (a) What is the probability that…

A First Course in Probability (10th Edition)

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Author:Sheldon Ross

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Chapter1: Combinatorial Analysis

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A box in a supply room contains 24 compact fluorescent lightbulbs, of which 8 are rated 13-watt, 9 are rated 18-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 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?

Expert Solution

Step 1

AS PER POLICY I HAVE CALCULATED FIRST 3 SUBPARTS PLZ REPOST FOR OTHER PARTS

here from given information

box contains total 24 light bulbs

8 are 13 watt rated

9 are 18 watt rated

7 are 23 watt rated

here use hypergeometric distribution

$p (x) = \frac{(\begin{matrix} S \\ x \end{matrix}) (\begin{matrix} N - S \\ n - x \end{matrix})}{(\begin{matrix} N \\ n \end{matrix})}$

N = #population

n = #sample

x= #favourable in sample

S =#favourable in population

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(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?