Probability question from Official Guide

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Probability question from Official Guide

by aimscore » Tue Sep 14, 2010 10:22 am
Hi,

This question is from the Official Guide 12th edition.

A = {2, 3, 4, 5}
B = {4, 5, 6, 7, 8}
Two integers will be randomly selected from the sets
above, one integer from set A and one integer from
set B. What is the probability that the sum of the two
integers will equal 9 ?
(A) 0.15
(B) 0.20
(C) 0.25
(D) 0.30
(E) 0.33

The answer is B.

The explantion provided by OG is:

The total number of different pairs of numbers,
one from set A and one from set B is (4)(5) = 20.
Of these 20 pairs of numbers, there are 4 possible
pairs that sum to 9: 2 and 7, 3 and 6, 4 and 5, and
5 and 4.
Thus, the probability that the sum of the
two integers will be 9 is equal to 4/20= 0.2
The correct answer is B.

As per my understanding I get 3 pairs :ie: 2 and 7, 3 and 6, 4 and 5.

I dont understand why the explanation takes into account 5 and 4. if the explanation says 5 and 4 is a pair then going by that fashion, 6 and 3, 7 and 2 should be two more pairs.

Can someone pls explain this to me.

Thanks
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by diebeatsthegmat » Tue Sep 14, 2010 10:40 am
aimscore wrote:Hi,

This question is from the Official Guide 12th edition.

A = {2, 3, 4, 5}
B = {4, 5, 6, 7, 8}
Two integers will be randomly selected from the sets
above, one integer from set A and one integer from
set B. What is the probability that the sum of the two
integers will equal 9 ?
(A) 0.15
(B) 0.20
(C) 0.25
(D) 0.30
(E) 0.33

The answer is B.

The explantion provided by OG is:

The total number of different pairs of numbers,
one from set A and one from set B is (4)(5) = 20.
Of these 20 pairs of numbers, there are 4 possible
pairs that sum to 9: 2 and 7, 3 and 6, 4 and 5, and
5 and 4.
Thus, the probability that the sum of the
two integers will be 9 is equal to 4/20= 0.2
The correct answer is B.

As per my understanding I get 3 pairs :ie: 2 and 7, 3 and 6, 4 and 5.

I dont understand why the explanation takes into account 5 and 4. if the explanation says 5 and 4 is a pair then going by that fashion, 6 and 3, 7 and 2 should be two more pairs.

Can someone pls explain this to me.

Thanks
A+B will have 20 pairs, ( 2 can add to any number in B thus we will have 5 pair added with 2 and so on the same with 3,4,5 so total = 4*5=20 )
A=(2,3,4,5)
B=({4, 5, 6, 7, 8} will have only 4 pair A+B =2+7, 3+6,4+5,5+4
thus answer is B

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by aimscore » Tue Sep 14, 2010 12:01 pm
diebeatsthegmat,

Was making a very stupid mistake. Understood the solution.
Thanks anywyas:)