7 coins are tossed simultaneously. What is the probability that a tail appears an odd number of times?

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7 coins are tossed simultaneously. What is the probability that a tail appears an odd number of times?

As 7 coins are tossed simultaneously the total number of outcomes are $2^{7}=128$ .
The favourable number of outcomes that a tail appears an odd number of times will be, ${ }^{7} \mathrm{C}_{1}+{ }^{7} \mathrm{C}_{3}+{ }^{7} \mathrm{C}_{5}+$ ${ }^{7} \mathrm{C}_{7}=64$
Thus, the probability
$\begin{array}{l} =\frac{\text { The favourable outcomes }}{\text { The total number of outcomes }} \\ =\frac{64}{128} \end{array}$
$=\frac{1}{2}$
Hence, the probability is $_{1 / 2}$ .