Independent Events: Coins

P(A ∩ B) = P(A) × P(B)

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

Specific Sequence: HTHT

What is a "specific sequence"?

We want the flips to come out in an exact order: Heads first, then Tails, then Heads, then Tails. Any other outcome (like THHT or HTHH) does NOT count.

Why does independence matter here?

Since each flip is independent, we can multiply the probability of each individual outcome: P(H) × P(T) × P(H) × P(T). Each factor is ½.

A common misconception:

Some people think "alternating" patterns like HTHT are "less random" or harder to get than "clumpy" patterns like HHTT. This is false!Every specific 4-flip sequence has the exact same probability.

The Sequence

Flip 1

Flip 2

Flip 3

Flip 4

Probability Calculation

Each flip has probability 1/2

P(H) = 1/2 and P(T) = 1/2

Multiply all probabilities

Result:

Important Observation

ANY specific sequence of 4 flips has probability 1/16. HHHH, TTTT, HTTH, THHT - they are all equally likely! There is no "lucky" or "unlucky" sequence.