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Each of the 30 students in a class is either male or female

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Each of the 30 students in a class is either male or female

by BTGmoderatorDC » Fri Jan 19, 2018 10:07 pm
Each of the 30 students in a class is either male or female, and has blonde, brown, or red hair. If one student is to be randomly selected from the class, what is the probability that the student will either be female or have brown hair?

(1) The probability that the student will be both female and have brown hair is 0.1
(2) The probability that the student will be female minus the probability that the student will have brown hair is 0.25

How will i find the sufficient statement?

OA E
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by Jay@ManhattanReview » Tue Jan 23, 2018 6:32 am
lheiannie07 wrote:Each of the 30 students in a class is either male or female, and has blonde, brown, or red hair. If one student is to be randomly selected from the class, what is the probability that the student will either be female or have brown hair?

(1) The probability that the student will be both female and have brown hair is 0.1
(2) The probability that the student will be female minus the probability that the student will have brown hair is 0.25

How will i find the sufficient statement?

OA E
Say the probability that the selected student is a female = p(f), the probability that the selected student is a female with brown hair = p(fb), and the probability that the selected student is a male with brown hair = p(mb).

We have to get the value of p(f) + p(mb).

(1) The probability that the student will be both female and have brown hair is 0.1.

=> p(fb) = 0.1. We can't get the value of p(f) + p(mb). Insufficient.

(2) The probability that the student will be female minus the probability that the student will have brown hair is 0.25.

=> p(f) - p(fb) - p(mb) = 0.25. We can't get the value of p(f) + p(mb). Insufficient.

(1) and (2) together

From (1), we have p(fb) = 0.1 and from (2), we have p(f) - p(fb) - p(mb) = 0.25. Thus, p(f) - 0.1 - p(mb) = 0.25 => p(f) - p(mb) = 0.35. We still can't get the value of p(f) + p(mb). Insufficient.

The correct answer: E

Hope this helps!

-Jay
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