Independent Events: Coins

P(A ∩ B) = P(A) × P(B)

Calculator Dice Coins Marbles Cards Learn

Two Heads in a RowTwo Heads Specific Sequence (HTHT)Sequence Multiple Coin FlipsMulti-Flip

Two Heads in a Row

Why are coin flips independent?

A coin has no memory. It doesn't "know" what happened on the previous flip. Getting heads on flip 1 doesn't make heads more or less likely on flip 2. Each flip is a fresh 50/50 chance.

What does "two heads in a row" mean mathematically?

We need BOTH events to happen:

• Event A: First flip is heads
• Event B: Second flip is heads

We want P(A AND B), which for independent events = P(A) × P(B).

The Multiplication Rule for Independent Events:

This only works because A and B don't affect each other!

Two Coin Flips

First Flip: Heads

Second Flip: Heads

Result:

All Possible Outcomes

1/4

Each outcome has equal probability of 1/4