AI Grounds
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AI Grounds
These interactive lessons need a larger screen. Please continue on a desktop or laptop computer.
Guided discovery
Select outcomes. Count what belongs to each event.
Two fair, independent dice give 36 equally likely ordered outcomes. A+B means both events; — means neither. ✓ marks outcomes counted by A.
| 1st / 2nd | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|
| 1 | (1,1)— | (1,2)— | (1,3)— | (1,4)— | (1,5)— | (1,6)A |
| 2 | (2,1)B | (2,2)B | (2,3)B | (2,4)B | (2,5)A+B | (2,6)B |
| 3 | (3,1)— | (3,2)— | (3,3)— | (3,4)A | (3,5)— | (3,6)— |
| 4 | (4,1)B | (4,2)B | (4,3)A+B | (4,4)B | (4,5)B | (4,6)B |
| 5 | (5,1)— | (5,2)A | (5,3)— | (5,4)— | (5,5)— | (5,6)— |
| 6 | (6,1)A+B | (6,2)B | (6,3)B | (6,4)B | (6,5)B | (6,6)B |
P(A) = |A| / |S|
6 / 36 ≈ 0.167
One event probability is its region size divided by all possible outcomes.
Outcomes in event A.
6/36
Sum is 7
Outcomes in event B.
18/36
First die even
The overlapping outcomes.
3/36
A ∩ B
Outcomes counted by this rule.
6/36
A: ≈ 0.167
Each simulated roll samples one ordered pair. Changing events or the rule starts a new sample; Clear rolls also resets the sample.
No rolls yet
Exact: 6 / 36 ≈ 0.167. Larger samples reduce sampling noise on average, but need not get closer at every step. Rolls use a repeatable pseudorandom stream, not physical dice.
A selects 6 of 36 outcomes. 0 simulated rolls; 0 hits.