If a and b are two integers randomly selected from the set 1 to 100

Question

If a and b are two integers randomly selected with replacement from the set 1 to 100, both inclusive, then what's the probability that a*b is divisible by 2?

A. 1/8
B. 1/4
C. 1/2
D. 9/16
E. 3/4

chetan2u · Accepted Answer

I believe the question means that a and b can be the SAME number too..

So, when will we have a*b as even --- When at least on of them is even
AND when is this NOT going to happen --- When none of them is even.

It is easier to find the second case, so let us see the ways in which a*b is Odd..... a and b both can be any of 50 Odd numbers = 50*50
Total ways to choose a*b = 100*100

Probability =  \frac{50*50}{100*100}=\frac{1}{4} .

Thus, the probability that a*b is divisible by 2 =  1-\frac{1}{4}=\frac{3}{4}

E

ScottTargetTestPrep · Answer

We can use the formula:

P(ab is divisible by 2) = 1 - P(ab is not divisible by 2)

“ab is not divisible by 2” means that we must select odd numbers for both a and b. Thus, P(ab is not divisible by 2) = P(a is odd and b is odd) = ½ x ½ = ¼. Therefore,P(ab is divisible by 2) = 1 - ¼ = ¾.

Answer: E

gurmukh · Answer

Following are the choices for two numbers taken out
EE EO OE OO
Out of this three are favourable
So answer is 3/4
Option E

Posted from my mobile device

CalvinHobbesIn · Answer

This is an important assumption - that repetition is allowed. Otherwise, the solution would be
P = 1-P(both odd) = 1-(50C2 / 100C2)

I did this mistake. Thanks Chetan!

akshitab2912 · Answer

In such a question how do we decide whether replacement is allowed or not?

IanStewart · Answer

The question absolutely needs to tell you that, or else there's no way to guess what the answer should be. This is not a well-written question.

chetan2u · Answer

Hi
The question requires to specify that. I too start with in my solution that I believe it that way because that is the only way you can get one of the options as an answer.

imgauravrawat · Answer

we can do it by this way =
we can make 4 option because we only have to select 2 number 
1) odd*odd
2) even* even
3)even*odd
4) odd*even

we don't get only in 1 case and from rest we can get even 
so the answer will 3/4
(E)

CrackverbalGMAT · Answer

CONCEPT : Probability P(Event E not occurring) = 1-P(E) SOLUTION: Probability (ab not divisible by 2) = P(Odd a)*P(Odd B) =1/2 * 1/2 =1/4 P(ab divisible by 2)=1-1/4=3/4 (E) Hope this helps

Devmitra Sen

SHYAM23 · Answer

if a and b are two integers randomly selected with replacement from the set 1 to 100, both inclusive, then what's the probability that a*b is divisible by 2?

A. 1/8
B. 1/4
C. 1/2
D. 9/16
E. 3/4

1 to 100 how many number are divided by 2
so lets no from 1to 10
from 1 to 10
8,4,6,2,10 so the probablity is 5/10=1/2
so for 1 to 100 probablity =1/2^2
=1/4
1-1/4=3/4

bumpbot · Answer

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If a and b are two integers randomly selected from the set 1 to 100

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If a and b are two integers randomly selected from the set 1 to 100

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