Events on the two-dice grid
Roll two dice. The sample space is the 36 ordered pairs (first die, second die), all equally likely. An event is just a set of squares on this grid. Pick two events and combine them.
From the slides: Sets: the language of events and Probability and what happens when you learn something.
|A|
|B|
|A ∩ B|
|A ∪ B|
P(selected set)
Simulated frequency
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What to notice
- “A or B” is A ∪ B, “both” is A ∩ B, “not A” is Ac. Every English sentence about the dice becomes a set of squares.
- Inclusion–exclusion, |A ∪ B| = |A| + |B| − |A ∩ B|, is checked live for every pair of events.
- Try A = “sum is 7”, B = “sum is 6”: the diagonals never touch, so A ∩ B is empty — mutually exclusive events.
- A given B greys out everything outside B. Conditioning shrinks the sample space to B and counts inside it: P(A | B) = |A ∩ B| / |B|. Try A = “sum is 8” given B = “first die is 3”.