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Table 1 Examples of probability calculations for coin tosses, based on Pascal’s triangle

From: The history of risk: a review

Number of coin tosses (equal to row numbers in Pascal’s triangle)

Possible outcomes (H, heads; T, tails)

Number of possible outcomes in Pascal’s triangle

1

H

1

T

1

2

HH

1

HT, TH

2

TT

1

3

HHH

1

HHT, HTH, THH

3

HTT, THT, TTH

3

TTT

1

4

HHHH

1

HHHT, HHTH, HTHH, THHH

4

HHTT, HTHT, HTTH, THHT, THTH, TTHH

6

HTTT, THTT, TTHT, TTTH

4

TTTT

1