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February 28th, 2014, 07:16 PM   #1
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Probability Problem / Insurance problem

Not sure what to title this post. It's from basic probability but it's been about a year and a half. I'm studying for exam P and experienced this problem at the end of the section I'm reading and am having trouble figuring out precisely what to do. I know the answer is 0.5 but not clear on how to get there. I tried 2 ways and got 97/144 once and 23/36 another time. So here is the question.

An insurer o ffers a health plan to the employees of a large company. As
part of this plan, the individual employees may choose exactly two of the
supplementary coverages A; B; and C; or they may choose no supplementary
coverage. The proportions of the company's employees that choose coverages
A; B; and C are 1/4, 1/3, and 5/12, respectively.
Determine the probability that a randomly chosen employee will choose no
supplementary coverage.

Any insight will be appreciated.
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March 1st, 2014, 01:00 PM   #2
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Re: Probability Problem / Insurance problem

1/4 + 1/3 + 5/12 = 1. Since the employees who chose a plan had to choose 2, divide by 2 to get fraction of employees who chose plans (1/2). The remaining 1/2 chose no plan.
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March 1st, 2014, 02:50 PM   #3
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Re: Probability Problem / Insurance problem

Thanks so much. I had considered that but it seemed way too simple. I guess overthinking is gonna be a problem on exam P.
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