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Identical results in $6$ tosses

ProbabilityEasy

A fair coin is tossed $6$ times, independently. What is the probability that all $6$ results are the same (all heads or all tails)? Give a fraction in lowest terms.

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Hint

Count the favorable sequences and compare with the total number of equally likely sequences.

Solution

There are $2^{6} = 64$ equally likely sequences of results.
Exactly $2$ of them are constant: all heads and all tails.
The probability is $\frac{2}{64}$ , which reduces to $\frac{1}{32}$ .
The answer is $\frac{1}{32}$ .

Answer: $\frac{1}{32}$

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