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by jeph86 » Sat Jun 04, 2016 7:30 am
Three integer from 1 to 100 are randomly selected such that one integer can be selected multiple times. what is the probability that the sum of the three integers will be even.

A) 7/32
B) 1/4
C) 9/32
D) 3/16
E) 1/2

this question come from a youtube complex proability question. when he solve it, He selected E. when I did it i did not find any in the answer choice i got 7/8

I start with these option: EEE or OOE or OEE please help.
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by GMATGuruNY » Sat Jun 04, 2016 8:19 am
Since there are 50 odd numbers and 50 even numbers:
P(odd number) = P(even number) = 1/2.

Ways to get an ODD sum:
3 odd numbers
1 odd number, 2 even numbers

Ways to get an EVEN sum:
3 even numbers
1 even number, 2 odd numbers

Since the probabilities in red are equal and the probabilities in blue are equal, there is a 50% chance that the sum will be ODD and a 50% chance that the sum will be EVEN.

Thus:
P(odd sum) = 1/2.

The correct answer is E.
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by GMATGuruNY » Sat Jun 04, 2016 8:35 am
Alternate approach:

The sum will be odd if all 3 numbers selected are odd or if exactly 1 number selected is odd.
Let O = odd and E = even.
Since there are an equal number of odd numbers and even numbers in the box, P(O) = 1/2 and P(E) = 1/2.

Probability all 3 are odd:
P(OOO) = 1/2 * 1/2 * 1/2 = 1/8

Probability exactly 1 is odd:
P(OEE) = 1/2 * 1/2 * 1/2 = 1/8
Since EOE and EEO are also good outcomes, we multiply this result by 3:
3 * 1/8 = 3/8

Since we'll get a good outcome if all 3 numbers selected are odd OR if exactly 1 number selected is odd, we add the fractions:
1/8 + 3/8 = 4/8 = 1/2.

The correct answer is E.
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by [email protected] » Sat Jun 04, 2016 9:12 am
Hi jeph86,

Back in March, you posted that you had scored Q21 on your first practice CAT and that your overall score goal was a 600.

1) Have you taken any CATs since then? How did you score on each (including the Quant and Verbal Scaled Scores)?
2) Is your goal score still a 600?

I ask these questions because you won't have to correctly answer any questions of this difficulty level to score a 600 on Test Day, so you might be better served focusing on other concepts/questions types.

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by jeph86 » Sat Jun 04, 2016 9:49 am
Hi Rich,

Thank you for responding. yes my target is still 600. I think my problem is when I am practicing. if I miss a hard question, I spent a long long long time trying to figure thing out. I end up running out time. I have not take the CAT. I will take it this weekend. probability is the last concept i need to learn. I thought math was going to be strong for me. verbal is my weakness for sure. I m not doing great in the math concept. I have not studied the verbal section. I have goal to take it in July 2nd because my deadline is July 15 to apply. I will take the whole CAT this weekend and post my score.

Thanks for the feedback.
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by Matt@VeritasPrep » Tue Jun 07, 2016 10:45 pm
Another way to think of this: you're equally likely to select an odd or an even each time. Given three numbers, we know

prob(all odd) = prob(all even)
prob(1 odd) = prob(1 even)

and those are the only four cases!

We want (p(all odd) + p(1 odd)) / total

and since we have exactly half the total cases in the numerator, our p = 1/2.
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