Aptitude - Probability - Discussion

3 cases.

even* odd=even.
even * even =even.
odd * even= even.
add all
(3/6*3/6)+3/6*3/6)+(3/6*3/6)=3/4.

We can do this question in two ways:

If we are looking at how many odd ways that better and easy to think :
1,3,5 are the odd digits in dice
to get odd both numbers should be odd
so the number of chances for the first number is 3,
and for second also 3.

Because 1*1,3*3 etc are also odd.
So favourable outcomes are 3*3=9.
prob=9/36 ->odd probability,
for prob(even)= 1-prob(odd).

Odd * Even = Even.

Total=(3+3+3)=9;
Even*odd=even
Total=(6+6+6)=18;
So here total odd number is (1,3,5);
And even (2,4,6);
Now E=27;
And Total=6*6=36
Prob=27/37=3/4 ans.

First, we have to select from any of the six sides then we have only three sides even or odd so 6c1*3c1.

Then we have 3 even and 3 odd for selection so 3c1*3c1 so final.

6c1 * 3c1+3c1 * 3c1/36.

The simple method is : we have 3 odd number(1, 3 ,5) and 3 even number(2, 4, 6);
We know that (even* even=even): = (3 even number * 3 even number=9));
(odd* even=even):= (3 odd number * 3 even number=9);
(even*odd=even):=(3 even number * 3 odd number=9);
Total even sum=9+9+9 = 27,
Total possiblity of two dice are = 6*6 = 36 (because each dice have 6 faces),
Therefore probablity=27/36 = 3/4.


Note: Here I have taken even*odd and odd*even because either of dice may contain even or odd;i.e: 1st dice contain 1 and second will contain 2 or 1st will contain 2 and 2nd will contain 1.

The answer should be 1/2.

Product = multiplication of both dice number is even.

I am not understanding this.

@All.

I have a more elegant solution.

Probability of occurrence of an odd number in one die is 3/6 or 1/2. In two die it will be 1/2+ 1/2 = 1/4.

So 1/4 is the total probability of occurrence of an odd number in both dies. Therefore, the probability of occurrence of even number as product will be 1 - 1/4 (since the product of odd-even and even-even is always even)= 3/4.

@Kanishk.

It's understandable.