$|t-h|$ is prime

Probability Level 3

A fair coin is flipped 10 times. What is the probability that the difference between the number of heads and the number of tails is a prime number ?

For example, if $h$ is the number of heads and $t$ is the number of tails, $\left | h-t \right |$ is a prime number.

Give your answer to three decimal places.

For more Permutations quizzes.

The answer is 0.410.

1 solution

Geoff Pilling
May 2, 2016

The difference between the number of heads and number of tails has to be an even number, and the only even prime is $2$ . So, we'd need to have either $6$ heads and $4$ tails or $6$ tails and $4$ heads. The number of ways we can achieve each of these is given by $\binom{10}{4}$ .

So, the probability is given by $\frac{ 2 * \binom{10}{4} }{2^{10}} = \boxed{0.410}$

∣ t − h ∣ |t-h| ∣ t − h ∣ is prime

For more Permutations quizzes.

The answer is 0.410.

1 solution

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$|t-h|$ is prime