Intersection: Coins

P(A ∩ B) - both conditions satisfied

All Three Coins Same

What does "all same" mean exactly?

All three coins must show the identical result. Either:

Any mixture like HHT, HTH, or THH does NOT count.

Why is this an intersection problem?

For all heads, we need three events to ALL happen:

This is P(H₁ ∩ H₂ ∩ H₃). Similarly for all tails.

Strategy: Break it into cases

We'll calculate P(all heads) and P(all tails) separately, then add them (they can't overlap — coins can't be all heads AND all tails!).

Green = All same (HHH or TTT)

Calculate P(all heads) using the multiplication rule

For all heads, we need head on coin 1 AND head on coin 2 AND head on coin 3. Since flips are independent, we multiply:

Calculate P(all tails) the same way

By the same logic:

Combine using the addition rule (OR)

"All same" means "all heads OR all tails". Since these events are mutually exclusive (can't have both at once), we simply add:

Result:

Let's verify by listing all 8 possible outcomes:

HHH ✓

HHT

HTH

HTT

THH

THT

TTH

TTT ✓

2 favorable outcomes ÷ 8 total outcomes = 2/8 = 1/4 ✓