Recall that the probability of a binomial distribution is given by
[tex]P(X=x)=^^nC_r\cdot p^x\cdot(1-p)^{n-x}[/tex]Where n is the number of trials, p is the probability of success, and x is the variable of interest.
nCr is the number of combinations.
For the given case, we have
n = 18
p = 0.8
x = 15
Let us find the probability P(X=15)
[tex]\begin{gathered} P(X=15)=^{18}C_{15}\cdot0.8^{15}\cdot(1-0.8)^{18-15} \\ P(X=15)=816\cdot0.8^{15}\cdot0.2^3 \\ P(X=15)=0.2297 \end{gathered}[/tex]Therefore, the probability P(X=15) is 0.2297