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Probability Problem

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Probability Problem

by tttrn333 » Mon Sep 19, 2011 4:05 am
Each of the 30 students in the class is either male or female and has blond, brown, or red hair. If one student is selected, what is he probability that this person will be either female or brown hair?

1) Probability that the student is both female and brown is .1
2) Probability that the student is female minus brown is .25

Why can't you it be C? Can we do XY=1/10 and X-Y=.25 and solve accordingly. Also, what is the significance of the 30 students? Seems to make statement B wrong no? Because 1/4 of 30 is not integer. The number of female minus he number of brown should be an integer.
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Source: — Data Sufficiency |
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by cans » Mon Sep 19, 2011 4:29 am
A) FB = .1 (Female and Brown)
Insufficient.
B) Female - Brown = .25 Insufficient
A&B) either F or B means: FB + (Female and not brown) + (brown and nor female)
insufficient
IMO E
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by KateRay » Tue Sep 27, 2011 10:10 pm
I often get struck in probability problems and take help from online tutors from tutorteddy...also take advantage of Khan videos.
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by Brian@VeritasPrep » Wed Sep 28, 2011 8:30 am
I wonder where this problem comes from because, like you said, you can't take 1/4 of 30... And statement 2 is written pretty poorly. I *think* it's trying to say that "the probability that the student is a female without brown hair is .25", but the way it's written I don't think rules out "Probability of female - probability of brown hair = .25".

But if we take it the way that we think it's intended, then both statements together give us:

Females with brown hair = 10% of the population
Females without brown hair = 25% of the population

So... Females (total) = 35% of the population
And.. Males of any hair color = 65% of the population

What we need, though, is the combination of "Females without brown hair (which we know is 25%)" + "Males with brown hair". And we don't know "Males with brown hair". We know that 60% of the total population is male, but with three hair colors to choose from we don't know how that 65% is allocated among males (are all males brown-haired? Are some blond, some red, and none brown?).


For these "how many have this trait but not that trait" type problems, it's most helpful to list what you know and what you need, often in table form (hard to draw here, but you could have rows "males, females, total" and columns "brown hair, not brown hair, and total" and fill in the cells that you know, deriving then those that you can to see which information you don't know).

Now...if this problem were better-written you'd be able to convert those percentages to numbers, which might help you eliminate noninteger possibilities. But as it is that's not in play here because you can't take 25%, 35% or 65% of 30...
Brian Galvin
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Chief Academic Officer
Veritas Prep

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