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multiple Q prob

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multiple Q prob

by maihuna » Fri Aug 14, 2009 9:06 am
An instructor has a question bank consisting of 300 easy True / False questions, 200 difficult True / False questions, 500 easy multiple choice questions and 400 difficult multiple choice questions. If a question is selected at random from the question bank, what is the probability that it will be an easy question given that it is a multiple choice question?
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Re: multiple Q prob

by DanaJ » Fri Aug 14, 2009 11:52 am
maihuna wrote:An instructor has a question bank consisting of 300 easy True / False questions, 200 difficult True / False questions, 500 easy multiple choice questions and 400 difficult multiple choice questions. If a question is selected at random from the question bank, what is the probability that it will be an easy question given that it is a multiple choice question?
Confusing wording right there...

The most obvious thing to do is use the standard formula of favorable/total number. In this case, it would be 500/1400 = 5/14.

However, since you get the wording that you get, I can't help but wonder if there's more to it. What if the event of a question being easy and the event of a question being multiple choice are considered separately? If this is the case, hitting a question that has both attributes will be the product of two fractions:

total easy = 800 ---> P easy = 800/1400 = 8/14 = 4/7

total multiple = 900 ---> P multiple = 900/1400 = 9/14

Total P = 4/7 * 9/14 = 2/7 * 9/7 = 18/49.

I wouldn't expect this type of wording on the real thing; it's waay to confusing.
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Re: multiple Q prob

by maihuna » Fri Aug 14, 2009 10:46 pm
DanaJ wrote:
maihuna wrote:An instructor has a question bank consisting of 300 easy True / False questions, 200 difficult True / False questions, 500 easy multiple choice questions and 400 difficult multiple choice questions. If a question is selected at random from the question bank, what is the probability that it will be an easy question given that it is a multiple choice question?
Total P = 4/7 * 9/14 = 2/7 * 9/7 = 18/49.

I wouldn't expect this type of wording on the real thing; it's waay to confusing.
Let F: Event that a multiple choice question is selected.
E: An Easy question is selected.

n(S)= total events = 300+200+500+400 = 1400
n(E) = total easy Q = 300+500 = 800
n(F) = total multiple Q = 500+400 = 900
n(E&F) = Easy Multiple Q = 500

P(E) = 8/24, P(F) = 9/14, P(E&F) = 5/14

P(E|F) = P(E&F)/P(F) = (5/14)/(9/14) = 5/9
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