The sample space S for the three tosses of the coin is:
Let "W" be a random variable giving the number of heads minus the number of tails in three tosses of a coin, we assign a value of "\\omega" of "W" to each sample point in the following way:
The sample space for "W" is
corresponding to "3T,1H2T,2H1T," and "3H" respectively.
"P(1\\ head\\ \\&\\ 2\\ tails)=\\binom{3}{1}({1 \\over 2})^1({1 \\over 2})^2={3 \\over 8}"
"P(2\\ heads\\ \\&\\ 1\\ tail)=\\binom{3}{2}({1 \\over 2})^2({1 \\over 2})^1={3 \\over 8}"
"P(3\\ heads\\ \\&\\ 0\\ tails)=\\binom{3}{3}({1 \\over 2})^3({1 \\over 2})^0={1 \\over 8}"
"P(W=-3)={1 \\over 8}"
"P(W=-1)={3 \\over 8}"
"P(W=1)={3\\over 8}"
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