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Coin Flip Probability

Master coin probability step by step

Calculator Dice Coins Marbles Cards Learn

Single Flip1 Flip Two Flips2 Flips Three Flips3 Flips Biased CoinsBiased

Building the Sample Space

The Pattern Continues

With each additional flip, the sample space doubles in size:

1 flip:

2 flips:

3 flips:

All 8 Outcomes

HHH

3H

HHT

2H

HTH

2H

HTT

1H

THH

2H

THT

1H

TTH

1H

TTT

0H

Distribution by Number of Heads

0 Heads:TTT= 1 outcome

1 Head:HTT, THT, TTH= 3 outcomes

2 Heads:HHT, HTH, THH= 3 outcomes

3 Heads:HHH= 1 outcome

Notice the pattern: 1, 3, 3, 1. This is row 3 of Pascal's Triangle!

Scenario: Getting All Heads (HHH)

Alternative: Multiplication Rule

Since flips are independent, we can multiply individual probabilities:

Scenario: Getting At Least 2 Heads

"At least 2 Heads" means 2 or 3 Heads:

HHH

HHT

HTH

HTT

THH

THT

TTH

TTT

Three-Flip Probability Summary

Event	Count	Probability
All Heads (HHH)	1
Exactly 2 Heads	3
Exactly 1 Head	3
All Tails (TTT)	1
At least 1 Head	7

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