Aptitude - Probability - Discussion

1 2 3 4 5 6
---------------------

1- 2 3 4 5 6 7

2- 3 4 5 6 7 8

3- 4 5 6 7 8 9

4- 5 6 7 8 9 10

5- 6 7 8 9 10 11

6- 7 8 9 10 11 12
using this table ec can do any sort of problems
e.g; we need sun 7 means check in table that how many times it comes
it is 6 there fore 6/36

P(odd) = 1/2
P(even) = 1/2
u will get an even number in three ways: odd*even
or even*odd or even * even
Hence the required probability =(1/2*1/2) +(1/2*1/2) + (1/2*1/2)
= 3*1/4
= 3/4

We can do this in the following way.

Getting an even product can be done in 3 ways

E*E=E;
E*O=E;
O*E=E;
(3C1/6C1)*(3C1/6C1)=9/36;
E*O=E;
(3C1/6C1)*(3C1/6C1)=9/36;
O*E=E;
(3C1/6C1)*(3C1/6C1)=9/36;
TOTALLY=
3*9/36= 3/4

Dice contain 1,2,3,4,5,6 faces
from this 2,4,6 are even.
so product even is possible when,
even * even + odd * even + even * odd
so 1 has 3 chances of getting even i.e (1*2 ,1*4, 1*6)
2 has 6 chances
3 has 3
4 has 6
5 has 3
6 has 6

so total possible even products are= 3+6+3+6+3+6 => 27
ans : 27/36
=>3/4

Another method:

The product will only by odd if the both dies are odd. P(1st Dice is odd) = 1/2 P(2nd Dice is odd) = 1/2.

1/2 * 1/2 = p both are odd hence product is odd as both rolls are independent events. P(odd product) = 1/4

Hence p(even product) = 1 - 1/4 = 3/4.

I do not understand because it is too lengthy process. Please tell the shortcuts.

Hi @Anusha,

I will try to make you understand the concept.

Probability is n(e)/n(S). here n(S) = 6*6 = 36.

To get n(e) i.e even product, we have to multiply odd with even or even with even.

Therefore, for odd with even we get,

1*2=2(product is even).
1*4.
1*6.

Therefore 3 combinations per odd number.

Similarly (do the same with 3 and 5) we get 3*3=9 combinations
for even with even: we get,

2*1.
2*2..till 2*6.

Therefore total 6 combinations with 3 even numbers, doing the same with 4 and 6 we get 6+6+6=18 combinations. Total n(e) =odd*even+even*even=9+18.

Substituting this value in n(e)/n(s) = 27/36 or 3/4.

Still it takes long time know?

I am getting concept but say in short way.

1st dice * 2nd dice.
Even*even = even.
Even*odd = even.
Odd*even = even.

So, 3/6 * 3/6 + 3/6 * 3/6 + 3/6 * 3/6 = (3*3*3)/(6*6) = 3/4.

Hi @bharath. K.

I am not understand below line.
n(S) = 6*6 = 36.

Why we are taking 6*6?