If one number is to be chosen at random from the integers 0 through 9

Question

If one number is to be chosen at random from the integers 0 through 9 and if a second number is to be chosen at random from the integers 0 through 9, what is the probability that the product of the two numbers will be even?

A. 2/9
B. 1/4
C. 1/2
D. 3/4
E. 7/9

A. 2/9
B. 1/4
C. 1/2
D. 3/4
E. 7/9

Bunuel · Accepted Answer

The only way for the product NOT to be even is if both chosen numbers are odd. The probability of that is 1/2 * 1/2 = 1/4. Therefore, the probability that the product will be even is 1 - 1/4 = 3/4.

Answer: D.

playthegame · Answer

Source is GMAT Focus prep tests / mock test....I could not find a way to add source.....or difficulty.

aniruddharora · Answer

Chosing First

Even || Odd
0.5   || 0.5

Chosing Second

Even -> Even 0.5*0.5 (Result Even)
Even - > Odd 0.5*0.5 (Result Even)

Odd - > Even 0.5*0.5 (Result Even)
Odd - > Odd 0.5*0.5 (Result Odd)

So for even 0.25 + 0.25 + 0.25 = 0.75

ronyweasley99 · Answer

Hello guys!

I don't know if this is a rule, but I got to D this way:

0 1 2 3 4 5 6 7 8 9

0* any of 10 =  100 % Even
1* any of 10 = 50% Even
2* any of 10 =  100 % Even
3* any of 10 = 50% Even
4* any of 10 =  100 % Even
5* any of 10 = 50% Even
6* any of 10 =  100 % Even
7* any of 10 = 50% Even
8* any of 10 =  100 % Even
9* any of 10 = 50% Even

Total  possible : 1000%
 All Possibilities to EVEN : 750% = 3/4 of possible

Am I right?

Thank you!

poojaarora1818 · Answer

Solution

Scenario 1

The probability of selecting two odds = 1/2 * 1/2 = 1/4

Scenario 2

The probability of selecting two evens= 1/2 * 1/2 = 1/4

Scenario 3

The probability of selecting one even and one odd = 1/2 * 1/2 = 1/4

If we add Scenario 1 + 2 + 3 we get  1/4 + 1/4 + 1/4 = 3/4

Hence, option D

thr3at · Answer

How can a product of 2 Odd number be even?

poojaarora1818 · Answer

The probability of selecting any even no. from the range 0-9 is 5/10 which is 1/2 in either case. Let's consider that the even nos. from the list is 0,2,4,6,8, which is five favorable outcomes divided by the total outcomes which is ten. It's the probability of selecting the even nos. from the range 0-9 not the product of two even nos. I hope that I can make my point clear.

egunckel10 · Answer

I believe I found a faster approach for this question.

The key for me was realizing that the product of two numbers from the sets given is always even UNLESS both of the numbers are odd.

Therefore, the probability that the product of two numbers from those sets is even will be 1- (Probability of selecting an odd number*Probability of selecting an odd number).

Since half of the numbers are odd, the probability of selecting an odd number is 5/10

So we have:

Probability that the product of two numbers from those sets is even= 1- 
Probability that the product of two numbers from those sets is even=1- 
Probability that the product of two numbers from those sets is even=3/4

reeyab · Answer

I thought the wording "one number" and "second number" meant that they were saying 2 different numbers :')

phoenixvr106 · Answer

From 0 to 9 there are 10 integers.

To get an even outcome, the operation has to be:

even * even = 5*5
even * odd = 5*5
odd * even = 5*5

add all of the above and divide by total outcomes (which is 10 * 10)

= (25 + 25 + 25)/100 =0.75 or 3/4

Pif96 · Answer

Easily,

Even * Even = Even
Even* Odd =Even
Odd*Even = Even
Odd*Odd= Odd

--> 3 scenario of 4 result in Even --> 3/4

tabishminto · Answer

Three cases

1. E * E Probability 1/2*1/2 = 1/4
2. E * O Probability 1/2*1/2 = 1/4
3. O * E Probability 1/2*1/2 = 1/4

Total Probability =1/4+1/4+1/4 = 3/4

GMATinsight · Answer

FOr product to be even, atleast one of teh chosen numbers should be even

Probability of both numbers to be odd = (1/2)*(1/2) = 1/4

Probability of At least one of them to be even = 1- (1/4) = 3/4

Answer: Option D

MrinmoyNegel · Answer

Correct me if I am wrong :

Question Stated is 2nd number picked up from the set.. which intuitively should mean number apart from the first selection. 
given that the prob for the first selection of ODD should be 1/2 and for the second should be 4/9 .. should BOTH odd selection should be 4/18..
Why should we assume that the 1st number selected in first case is available for selection in the second selection also ?

Bunuel · Answer

We are given that one number is selected from 0 through 9, and another from the same range. Why can’t both numbers be the same? Imagine two people are selecting numbers, couldn’t they select the same number?

If one number is to be chosen at random from the integers 0 through 9

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If one number is to be chosen at random from the integers 0 through 9

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