Intersection: Dice

P(A ∩ B) - outcomes satisfying BOTH conditions

Calculator Dice Coins Marbles Cards Learn

Even AND Greater Than 3Even & GT3 Prime AND OddPrime & Odd Less Than 4 AND OddLT4 & Odd

First, Let's Review: What is a Prime Number?

Definition:

A prime number is a number greater than 1 that can only be divided evenly by 1 and itself.

Checking numbers 1-6:

• 1 — Not prime (by definition, primes must be > 1)
• 2 — Prime ✓ (only divisible by 1 and 2)
• 3 — Prime ✓ (only divisible by 1 and 3)
• 4 — Not prime (4 = 2 × 2)
• 5 — Prime ✓ (only divisible by 1 and 5)
• 6 — Not prime (6 = 2 × 3)

Primes on a die: 2, 3, 5

Example: Rolling Prime AND Odd

Question

What is the probability of rolling a number that is both prime AND odd?

A: Prime Numbers

✓

Primes: 2, 3, 5

B: Odd Numbers

✓

Odd: 1, 3, 5

Which numbers are in BOTH groups?

• 1: Odd ✓, Prime ✗ (1 is not prime) — fails
• 2: Prime ✓, Odd ✗ (2 is even) — fails
• 3: Prime ✓, Odd ✓ — in both!
• 5: Prime ✓, Odd ✓ — in both!

A ∩ B: Prime AND Odd

✓

Only 3 and 5 are both prime AND odd.

Probability Calculation

2 numbers (3 and 5) satisfy both conditions out of 6 total:

Final Answer:

Interesting Math Fact

2 is the only even prime number!

Why? Any other even number can be divided by 2, so it's not prime. This is why 2 is sometimes called "the odd prime" — it's the only prime that isn't odd! In our problem, 2 fails the "odd" requirement even though it's prime.