Probability - Integer

Question

X=(1,2,3,4,5)
Y=(-9,-8,0,1,2,3)

If an Integer is randomly selected from Set X above and an Integer is randomly selected from Set Y. What is the probability that the product of the 2 integers will be positive?

A) 0
B) 2/3
C) 2/5
D) 1/2
E) 4/5

This is how I did which obviously is wrong so plz help me find my mistake.

As the product should be +ve, we cannot include -9 and -8 from Set Y. We also cannot include 0 as anything multiplied by 0 is a 0 which is neither +ve not -ve.
So for every option in Set X we have 3 possibilities (1,2,3).

Now, while making pairs we have 1*2, 1*3 and 2*3 counted twice so we'll take one pair and will be left with the following pairs.

1*1, 1*3
2*2, 2*3
3*3
4*1, 4*2, 4*3
5*1, 5*2, 5*3
In total 11 pairs out of 11C2 (as we want 2 out of 11 numbers including -8,-9 &0)

Pls help me understand if at all i am doing right..The answer is 1/2

cano · Answer

Since you have only positive integers in set X, the integers in set Y will make the product either positive or negative.
So no matter which integer you pick from X, for the purpose of probability you can take the following pairs:

X*(-9) = Negative
X*(-8) = Negative
X*0 = 0, no positive
X*1 = Positive
X*2 = Positive
X*3 = Positive

X being any integer from the X set. You could write out all the pairs, picking one integer from X and other from Y, but that is not necessary.
So you have 6 pairs, and 3 positive results. 3/6 = 1/2. Answer is D.

DeeptiM · Answer

You are assuming Set X to have only one number wherein it has 5 numbers..don't we need to multiply all the numbers in Set X with each and every number in Set Y to find out the +ve value??

cano · Answer

All right, let me explain it differently. You could write out all the pairs if you want, but you have to understand that it's time consuming.

Let's multiply Y*X.

-9*1=no positive, -9*2=no positive, -9*3=no positive, -9*4=no positive, -9*5=no positive
-8*1=no positive, -8*2=no positive, -8*3=no positive, -8*4=no positive, -8*5=no positive
0*1=no positive, 0*2=no positive, 0*3=no positive, 0*4=no positive, 0*5=no positive
1*1=positive, 1*2=positive, 1*3=positive, 1*4=positive, 1*5=positive
2*1=positive, 2*2=positive, 2*3=positive, 2*4=positive, 2*5=positive
3*1=positive, 3*2=positive, 3*3=positive, 3*4=positive, 3*5=positive

Now count: 15 no positives, 15 positives, total 30. Positives/total = 15/30 = 1/2.

cano · Answer

Since all integers of set X are positives, multiplying by each one of them or multiplying by only one of them will give you the same probability. In this problem the probability is defined by the number of positive integers in set Y against the total of integers in set Y.

Probability is like percentages, so sometimes you can make a shortcut. Whereas in combinatorics (either permutation or combination) you really need to count all the possibilities.

cano · Answer

Now that I read your first post again I can see that you are a little confused with probabilities and combinatorics. A great help for me was Veritas Prep Combinatorics and Probability book. But you can read for free in our GMAT Club Math book:

math-probability-87244.html
math-combinatorics-87345.html

It is critical that you understand the difference between probability and combinatorics problems. You should be able to read a problem and automatically identify how to approach the problem, or at least feel comfortable with the formulas and strategies for each problem.

DeeptiM · Answer

ook i got to know my mistake..i was counting 1*2 and 2*1 as same pairs..
I agree this approach is time consuming and liked ur earlier method..
thanks a ton for helping!!

cano · Answer

No problem. I'm glad that it helped you.

Probability - Integer

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