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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