Basic probability
Event space: The set of all possible outcomes. In this case, there are 36 possible rolls of the two dice.
Event: any subset of events from the event space. Here are some possible events: You roll (5,6). You roll (3,2). Your roll contains a 5. Your total roll is greater than 8.
For this simulation, we will represent these events more concisely as 56, 32, contains a 5, > 8.
The probability of an event is defined as follows: p(event) = # of outcomes where the event happens / total # of possible outcomes. For example, the probability of 56 is 1/36, because there is only one outcome where the roll is 56 (specifically, that outcome is the one where you roll 5 and 6!), while there are 36 total possible outcomes. We denote the probability of an event as p(event); thus, as a shorter way of saying "the probability of rolling 5,6 is 1/36", we would p(56) = 1/36.
Based on this definition, fill in values for the following probabilities (remember that hovering over the name highlights the relevant region of the event space):
p(32), p(contains a 5), p(> 8)
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
2
3
4
5
6
7
8
9
10
11
12
Even
Odd
1
2
3
4
5
6
1
2
3
4
5
6
7
8
9
10
11
2
3
4
5
6
7
8
9
10
11
12
13