What is the probability that the product of two integers (not necessar

Question

What is the probability that the product of two integers (not necessarily different integers) randomly selected from the numbers 1 through 20, inclusive, is odd?

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

Archit3110 · Answer

total integers ; 20
even =odd = 10
so to get product of two integers as odd both have to be odd ; we have 10 such integers
so P = 10/20; 1/2 ; 1st no
for second no ; 10/20 ; 1/2
so 1/2*1/2 ; 1/4

IMO B

m1033512 · Answer

I am a bit confused here .

No of ways to get odd product = 10C2 (10 odd number and we pick any 2 numbers)

and no of ways to get product of two integers = 20C2

so probab = 10C2/20C2

though not sure what is wrong with this approach

Can someone help please

Posted from my mobile device

ScottTargetTestPrep · Answer

Since odd x odd = odd and since half the integers 1 to 20 are odd, the probability of selecting two odd integers is 1/2 x 1/2 = 1/4.

Answer: B

gmat1393 · Answer

Hi  m1033512

Since repitition is allowed here we consider the formula n^r not nCr

Hope this helps

Michele4 · Answer

ScottTargetTestPrep   Bunuel   GMATNinja   VeritasKarishma  If it had been --> If one integer is randomly selected from 0 to 9 inclusive, and then a second integer is randomly selected from 0 to 9 inclusive, what is the probability that the product of the two integers is an even integer? 1/2?

GMATNinja · Answer

There are three ways to get an even product in your scenario: even x odd = even --> 1/4 probability if you're selecting from 0-9 inclusive odd x even = even --> 1/4 probability even x even = even --> 1/4 probability So the answer here would be 3/4. An easier way to do it: there's a 1/4 chance that the product is odd, right? (Odd x odd = 1/4, just like in the original question). So that means that there's a 3/4 chance that the product is even. I hope that helps a bit! (Wait... what am I doing in the quant forums?!?!

)

KarishmaB · Answer

Note that probability of selecting an even integer is 1/2 but the probability of the product being even is not 1/2. For the product to be even, all you need is one even integer. So even if the first integer you pick is odd, you can still have even product. Hence probability of even product will be higher than 1/2.

Of course, the probability of an odd product is easier to find because we must have BOTH integers odd. So odd product probability = 1/2 * 1/2 = 1/4

Probability of even product = 1 - 1/4 = 3/4

ScottTargetTestPrep · Answer

Reply:

Just as in the question, half of the integers between 0 and 9 are even and half are odd. Thus, we can reason exactly as in the solution and conclude that the probability of an odd product is 1/4. Then, the probability of an even product is 1 - 1/4 = 3/4.

bumpbot · Answer

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