four Youw light bulbs, contains 75-w bulbs. suppose that three bulbs are •abox in a certain supply room Three 60-w bulbs, and six randomly selected. a) what is probability that exactly two of the selected bulbs are rated 75-h b) what is the probability that all three of the selected bulbs have the same rating. C) what is the probability that one bulb of each type is selected_

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Chapter1: Combinatorial Analysis
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**Problem Statement:**

A box in a certain supply room contains four 40-watt lightbulbs, three 60-watt bulbs, and six 75-watt bulbs. Suppose that three bulbs are randomly selected.

a) What is the probability that exactly two of the selected bulbs are rated 75 watts?

b) What is the probability that all three of the selected bulbs have the same rating?

c) What is the probability that one bulb of each type is selected?

d) Suppose now that bulbs are to be selected one by one until a 75-watt bulb is found. What is the probability that it is necessary to examine at least six bulbs?
Transcribed Image Text:**Problem Statement:** A box in a certain supply room contains four 40-watt lightbulbs, three 60-watt bulbs, and six 75-watt bulbs. Suppose that three bulbs are randomly selected. a) What is the probability that exactly two of the selected bulbs are rated 75 watts? b) What is the probability that all three of the selected bulbs have the same rating? c) What is the probability that one bulb of each type is selected? d) Suppose now that bulbs are to be selected one by one until a 75-watt bulb is found. What is the probability that it is necessary to examine at least six bulbs?
Expert Solution
Given information

Given that 

Total lightbulbs = 4 + 3 + 6 = 13

40-w lightbulbs = 4

60-w lightbulbs = 3

75-w lightbulbs = 6

3 lightbulbs are selected at random 

nCr = n! / {r! * (n - r)!}

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