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When two dies are thrown, there are 36 possible outcomes. The first number represents the outcome of the first die and the second number represents the outcome of the second die.
(1,1),(1,2),(1,3),(1,4),(1,5),(1,6)
(2,1),(2,2),(2,3),(2,4),(2,5),(2,6)
(3,1),(3,2),(3,3),(3,4),(3,5),(3,6)
(4,1),(4,2),(4,3),(4,4),(4,5),(4,6)
(5,1),(5,2),(5,3),(5,4),(5,5),(5,6)
(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)
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How many outcomes are there in the sample space of rolling 2 dice?
11 outcomes if the dice are indistinguishable, 36 otherwise.
What is a possible set of outcomes?
The set of possible outcomes is the set of different ways in which an event might or might not happen. Take a very simple example: If you roll a dice you will roll a 6 or a 5 or a 4 or a 3 or a 2 or a 1. So there are 6 different possible outcomes, all of which are equally probable. If you roll 2 dice at the same time the possible total scores are are from 2 ( a 1 and a 1) to 12 (a 6 and a 6), so there are 11 possible outcomes, but not all equally probable.
If you roll 2 dice what is the probability of getting a 2 or 3?
When you roll 2 dice, the number of possible outcomes is 6x6 =36. From these 36 outcomes 3 are a 2 or 3 [(1,1), (1,2), (2,1)]. So the probability of getting a 2 or 3 is: P(2 or 3) = 3/36 = 1/12 = 0.08333... ≈ 8.3%
What is the probability of rolling a sum 10 with two dice?
3 times (out of 36) is the probablility Possible Outcome 1 - Dice 1: 4, Dice 2: 6 Possible Outcome 2 - Dice 1: 5, Dice 2: 5 Possible Outcome 3 - Dice 1: 6, Dice 2: 4
What is the probablity of rolling the sum of 12 on 2 dice?
There are 36 outcomes for rolling 2 dice, and there is 1 way that a 12 can occur which is 6,6. So, the probability of rolling the sum of 12 on 2 dice is 1/36.
