Coin Toss Probability Calculator

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Probability of head(s) and tail(s)
Probability of coin tosses with  
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Monte Carlo Coin Toss trials
  

Calculate the probability of flipping 1 head and 8 tails

List out ways to flip 1 head and 8 tails

HTTTTTTTT
THTTTTTTT
TTHTTTTTT
TTTHTTTTT
TTTTHTTTT
TTTTTHTTT
TTTTTTHTT
TTTTTTTHT
TTTTTTTTH

Calculate each coin toss sequence probability:

Calculate the probability of flipping a coin toss sequence of HTTTTTTTT

HeadsTailsTailsTailsTailsTailsTailsTailsTails
The probability of each of the 9 coin tosses is 1/2, so we have:
P(HTTTTTTTT)  =  1 x 1 x 1 x 1 x 1 x 1 x 1 x 1 x 1
  2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2

P(HTTTTTTTT)  =  1
  512

P(HTTTTTTTT) = 0.001953125

Calculate the probability of flipping a coin toss sequence of THTTTTTTT

TailsHeadsTailsTailsTailsTailsTailsTailsTails
The probability of each of the 9 coin tosses is 1/2, so we have:
P(THTTTTTTT)  =  1 x 1 x 1 x 1 x 1 x 1 x 1 x 1 x 1
  2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2

P(THTTTTTTT)  =  1
  512

P(THTTTTTTT) = 0.001953125

Calculate the probability of flipping a coin toss sequence of TTHTTTTTT

TailsTailsHeadsTailsTailsTailsTailsTailsTails
The probability of each of the 9 coin tosses is 1/2, so we have:
P(TTHTTTTTT)  =  1 x 1 x 1 x 1 x 1 x 1 x 1 x 1 x 1
  2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2

P(TTHTTTTTT)  =  1
  512

P(TTHTTTTTT) = 0.001953125

Calculate the probability of flipping a coin toss sequence of TTTHTTTTT

TailsTailsTailsHeadsTailsTailsTailsTailsTails
The probability of each of the 9 coin tosses is 1/2, so we have:
P(TTTHTTTTT)  =  1 x 1 x 1 x 1 x 1 x 1 x 1 x 1 x 1
  2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2

P(TTTHTTTTT)  =  1
  512

P(TTTHTTTTT) = 0.001953125

Calculate the probability of flipping a coin toss sequence of TTTTHTTTT

TailsTailsTailsTailsHeadsTailsTailsTailsTails
The probability of each of the 9 coin tosses is 1/2, so we have:
P(TTTTHTTTT)  =  1 x 1 x 1 x 1 x 1 x 1 x 1 x 1 x 1
  2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2

P(TTTTHTTTT)  =  1
  512

P(TTTTHTTTT) = 0.001953125

Calculate the probability of flipping a coin toss sequence of TTTTTHTTT

TailsTailsTailsTailsTailsHeadsTailsTailsTails
The probability of each of the 9 coin tosses is 1/2, so we have:
P(TTTTTHTTT)  =  1 x 1 x 1 x 1 x 1 x 1 x 1 x 1 x 1
  2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2

P(TTTTTHTTT)  =  1
  512

P(TTTTTHTTT) = 0.001953125

Calculate the probability of flipping a coin toss sequence of TTTTTTHTT

TailsTailsTailsTailsTailsTailsHeadsTailsTails
The probability of each of the 9 coin tosses is 1/2, so we have:
P(TTTTTTHTT)  =  1 x 1 x 1 x 1 x 1 x 1 x 1 x 1 x 1
  2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2

P(TTTTTTHTT)  =  1
  512

P(TTTTTTHTT) = 0.001953125

Calculate the probability of flipping a coin toss sequence of TTTTTTTHT

TailsTailsTailsTailsTailsTailsTailsHeadsTails
The probability of each of the 9 coin tosses is 1/2, so we have:
P(TTTTTTTHT)  =  1 x 1 x 1 x 1 x 1 x 1 x 1 x 1 x 1
  2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2

P(TTTTTTTHT)  =  1
  512

P(TTTTTTTHT) = 0.001953125

Calculate the probability of flipping a coin toss sequence of TTTTTTTTH

TailsTailsTailsTailsTailsTailsTailsTailsHeads
The probability of each of the 9 coin tosses is 1/2, so we have:
P(TTTTTTTTH)  =  1 x 1 x 1 x 1 x 1 x 1 x 1 x 1 x 1
  2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2

P(TTTTTTTTH)  =  1
  512

P(TTTTTTTTH) = 0.001953125


Calculate final probability:

P(HTTTTTTTT + THTTTTTTT + TTHTTTTTT + TTTHTTTTT + TTTTHTTTT + TTTTTHTTT + TTTTTTHTT + TTTTTTTHT + TTTTTTTTH)  =  1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1
  512

P(HTTTTTTTT + THTTTTTTT + TTHTTTTTT + TTTHTTTTT + TTTTHTTTT + TTTTTHTTT + TTTTTTHTT + TTTTTTTHT + TTTTTTTTH)  =  9
  512

P(HTTTTTTTT + THTTTTTTT + TTHTTTTTT + TTTHTTTTT + TTTTHTTTT + TTTTTHTTT + TTTTTTHTT + TTTTTTTHT + TTTTTTTTH) = 0.017578125

Coin Toss Probability Video