Problem 600

Solution. By the Bernoulli formula (19), we have $p_{5}(4)=C_{5}^{4} \cdot p^{4} \cdot q^{1}$. Here, the probability $p$ of hitting the target with one shot is unknown. To find it, we use the condition of the problem.

Let's denote the events:

$A_{1}$ - hitting the target with the first shot;

$A_{2}$ - hitting the target with the second shot;

$A_{1}+A_{2}$ - hitting the target at least once in two shots.

By formula (12), we find $p\left(A_{1}+A_{2}\right)=1-q^{2}$, i.e., $0.96=1-q^{2}$, from which $q=0.2$ and $p=1-q=0.8$. Therefore, $p_{5}(4)=5 \cdot(0.8)^{4} \cdot 0.2=$ $=0.4096$.

Answer. 0.4096.