213. Find the variance of the discrete random variable $X$ - the number of occurrences of event $A$ in five independent trials, if the probability of event $A$ occurring in each trial is 0.2.
Solution. The variance of the number of occurrences of an event in independent trials (with the same probability of the event occurring in each trial) is equal to the product of the number of trials by the probabilities of the event occurring and not occurring:

$$
D(X)=n p q .
$$

By the condition, $n=5 ; p=0.2 ; q=1-0.2=0.8$.

The required variance

$$
D(X)=n p q=5 \cdot 0.2 \cdot 0.8=0.8
$$