Aptitude - Probability - Discussion

Finally I found the answer of this question. It is very simple.

When two dice are tossed the total number of possibilities are 36.

Which means 6*6 =36. They are asked to find out the prime number. We know what is prime number, the number is divisible by the same number except 1.

In this concept the possibilities are
(1, 1), (1, 2), (1, 4), (1, 6), (2, 1), (2, 3), (2, 5), (3, 2), (3, 4), (4, 1), (4, 3),(5, 2), (5, 6), (6, 1), (6, 5).

from {(1,1), (1,2)... (6,6)}.

1+1=2, 1+2=3, 1+4=5, 1+6=7 the same way you can get the indivisible numbers expect the same number. So answer is 15/36 which is equal to 5/12 is the correct answer :-).

I am sure the answer is 1/6 for this as this event mentioned has something missing.

E = { (1, 1), (1, 2), (1, 4), (1, 6), (2, 1), (2, 3), (2, 5), (3, 2), (3, 4), (4, 1), (4, 3),
(5, 2), (5, 6), (6, 1), (6, 5) }

E(correct) = { (1,1), (1, 1), (1, 2), (1, 4), (1, 6), (2, 1), (2, 3), (2, 5), (3, 2), (3, 4), (4, 1), (4, 3), (5, 2), (5, 6), (6, 1), (6, 5) }
(1,1) will have a probability 2/12 rather than 1/12 un-like other pairs.

If you note (2,1) occurs and (1,2) also occurs and hence (1,1) due to dice A and additionally (1,1) due to dice B and hence the probability of this event is doubled.

The total no of unique combinations on throw of 2 dice is 36:

i.e. {(1,1),(1,2),(2,1),(1,3),(3,1),(2,2),(1,4),(4,1),(2,3),(3,2),(1,5),(5,1),(2,4),(4,2),(3,3),(1,6),(6,1),(2,5),(5,2),(3,4),(4,3),(2,6),(6,2),(3,5),(5,3),(4,4),(3,6),(6,3),(4,5),(5,4),(4,6),(6,4),(5,5),(5,6),(6,5),(6,6)}.

Out of these pairs, how many give us a prime number sum = 15.

i.e. {(1,1),(1,2),(2,1),(1,4),(4,1),(2,3),(3,2),(1,6),(6,1),(2,5),(5,2),(3,4),(4,3),(5,6),(6,5)}.

So, probability = 15/36 = 5/12.

@Rutvik.

There (1,1) consider only once because there is no difference between 1, 1 or 1, 1, but there is always a difference between 2, 5 or 5, 2.

Suppose dice 1 and dice 2 have the same no. Like (1, 1) how will you differentiate dice 1 and 2 but if the no. Are change like (1, 2) (2, 1) or (5, 2) (2, 5) you will differentiate dice 1 and 2. That's why.

I hope now you will understand.

@Vrushang.

In combination(1, 1) are same, in permutations order is impt ex: (1, 2),(2, 1).

Are same selection in combs we first 1 or 2, 2 or 1 is same comb. But in permutations the arrangement is imp 1, 2 it is different from 2, 1 first 1 is set in the row next second place 2 is set, first 2 is set in the row, next 1 is set in the row.

So I think you are understand.

The possible outcomes for the sum of two dice are as follows:

Sum: 2
Possible outcomes: (1, 1).

Sum: 3
Possible outcomes: (1, 2), (2, 1).

Sum: 5
Possible outcomes: (1, 4), (2, 3), (3, 2), (4,1).

Sum: 7
Possible outcomes: (1, 6), (2, 5), (3, 4), (4, 3), (5, 2), (6, 1).

Sum: 11
Possible outcomes: (5, 6), (6, 5).

So, there are 15 possible outcomes.

Hi sir, i am little bit poor in maths, what is the meaning of prime numbers...
{ (1, 1), (1, 2), (1, 4), (1, 6), (2, 1), (2, 3), (2, 5), (3, 2), (3, 4), (4, 1), (4, 3),
(5, 2), (5, 6), (6, 1), (6, 5) }

Why do choose those no only ?

Why don't you choose (6,6) (2,2)n etc

We get the number from the first dice = 1,2,3,4,5,6
And the same from the second dice.
We have prime numbers in both dice is 1, 2, 3, 4, 5 and a total of 1+2=3 is a prime number.
So, total 12.

We have 5 prime numbers and a total score number.
So, 5/12 is the answer.

Hey @Prasad,

Here is the clarification of your doubt. You have to choose those number of pairs whose sum is a prime number. If you choose (1, 3), (2, 2) & (3, 1) then their sum will be 4 which is not a prime number.

Thanks!

Prime number is nothing but a number which is divided by 1 or itself. For example 5 is divided by itself or only 1. So its called a prime number. 6 is not called a prime no because of it can divide by 2, 3. I hope now clear cut.