Coin Flip Probability

Master coin probability step by step

How Does the Sample Space Grow?

With 1 flip, we had 2 outcomes. With 2 flips, how many outcomes are there?

(2 outcomes)

For each outcome of the first flip, the second flip can be either H or T:

First Flip

Second Flip

H branches into HH and HT, T branches into TH and TT

Both Heads

Head then Tail

Tail then Head

Both Tails

Each flip has 2 outcomes, and the outcomes multiply together.

This is a common point of confusion! Here is why they are different:

First flip is Heads, Second flip is Tails

Flip 1: HFlip 2: T

First flip is Tails, Second flip is Heads

Flip 1: TFlip 2: H

Order matters! Each position in the sequence is a distinct flip with its own result.

"At least one Head" means 1 or more Heads:

2 Heads

1 Head

0 Heads

"At least one Head" is the complement of "no Heads" (which is TT):

Event	Outcomes	Count
Both Heads	HH	1
Both Tails	TT	1
Exactly 1 Head	HT, TH	2
At least 1 Head	HH, HT, TH	3