To find the variance of the number of heads in three tosses of a fair coin, we can use the properties of the binomial distribution. In this case, we have a binomial distribution with n=3 (number of trials) and p=1/2 (probability of success, which is getting a head for a fair coin).

The variance of a binomial distribution is given by the formula:

Variance=np(1−p)

where n is the number of trials and p is the probability of success for each trial.

In this case, n=3 and p=1/2.  Plugging these values into the formula, we get:

Variance=3×1/2×(1−1/2)=3×1/2 ×1/2 =3/4

So, the variance of the number of heads in three tosses of a fair coin is 3/4