(dcsports22 Asks:)
If I toss a coin three times, what is the probability that the coin will land heads up all three times?
(Jag Says:)
seven/eight
Properly, the number of possible outcomes of flipping a (nonbiased) coin is 2n, where n is the number of flips. (In general, the number of possible outcomes is xn, where x is the number of individual outcomes and n is the number of independent trials. For a coin x=2, for a standard die x=6, etc.)
The probability that a sequence will result is 1. (Flip a coin, and it`s going to land on heads or tails - it doesn`t vanish into thin air!) The probability of any given sequence (heads, tails, heads for example) is 1/(2n). The probability of any sequence EXCEPT tails, tails, tails would therefore be 1 - 1/(2n) = 7/8.
Don`t believe in math? Work it out by hand. Possible results (H=heads, T=tails):
HHH
HHT
HTH
HTT
THH
THT
TTH
TTT
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