Intersection: Dice

P(A ∩ B) - outcomes satisfying BOTH conditions

Example: Rolling Less Than 4 AND Odd

Question

What is the probability of rolling a number that is both less than 4 AND odd?

Strategy: Find numbers that pass BOTH tests

We need to find numbers that are (1) less than 4, AND (2) odd. Let's check each candidate.

✓

1, 2, 3 are all less than 4

✓

1, 3, 5 are odd (not divisible by 2)

Check each number from 1-6:

✓

Only 1 and 3 satisfy both conditions!

We found 2 favorable outcomes (1 and 3) out of 6 total:

Final Answer:

Here are some common "A AND B" combinations with dice. Notice how the intersection is always smaller than or equal to each individual set.

Condition A	Condition B	Pass Both
Even	> 3	{4, 6}
Prime	Odd	{3, 5}
< 4	Odd	{1, 3}
Even	Odd	∅ (empty)

Note: Even AND Odd has zero probability because no number can be both even and odd! These are mutually exclusive events.