If two six-sided dice are thrown, what is the probability

The attached file contains a simplified approach worth memorizing for calculating the probabilities involving the sum of 2 dices. As can be observed the sample space is 36 and there are 11 different sums including 2 3 4 5 6 7 8 9 10 11 12. The number of ways of getting each of these sums is 1 2 3 4 5 6 5 4 3 2 and 1 respectively. In order to calculate the probability for a given sum, simply divide the number of ways for getting that sum by the sample space (36). For example, we are being asked to calculate the probability of getting a sum of 6. A sum of 6 can be gotten in 5 ways. Therefore the probability is equivalent to 5/36.

I worked it out by working out all possible outcomes:
Dice 1 Dice 2
1 5
5 1
2 4
4 2
3 3
3 3

This gives you 6 outcomes from 36 combos - > 1/6, but the OA is 5/36. I assume this is because you aren't suppose to count 3-3 twice. My question is why not? You count 1-1, 2-2, 3-3 etc to get the 36 possibilities, so why do you not count 3-3 twice in the outcomes?

Help!

Skientist

When we roll two dice, there are 36 outcomes.

(1,1), (2,2) , (3,3) ... (6,6) are counted only once in those 36 possibilities..

(1,5) and (5,1) are two different possibilities and are two separate events


for example if the 2 dice are A & B,

there is a difference between saying 1 on die A, 5 on die B and saying 5 on die A, 1 on die B.

there is absolutely no such difference when you consider (3,3)

Easy peasy.

You have 6*6 possible outcomes, of which 5 are favourable:
5-1
1-5
4-2
2-4
3-3

So 5/36

youtube video dealing with probabilities involving sum of 2 and 3 dices: https://www.youtube.com/watch?v=iW2NQocbx3g&t=90s

Given that two six-sided dice are thrown and we need to find what is the probability that the sum of the numbers shown on the dice is six?

As we are rolling two dice => Number of cases = \(6^2\) = 36

Lets start writing the possible cases where sum of the two rolls = 6. Following are the possible cases:
(1,5)
(2,4)
(3,3)
(4,2)
(5,1)

=> 5 cases

=> Probability that sum of two rolls is 6 = \(\frac{5}{36}\)

So, Answer will be C
Hope it helps!

Watch the following video to learn How to Solve Dice Rolling Probability Problems

1x5 2x4 3x3 4x2 5x1. out of 36.