A sharp shooter can hit a target on a single trial with probability equal to 0.95. Suppose that the shooter fires 5 shots at the target.
a. what is the probability that the shooter will hit the target exactly two times?
+118616
$$P(Exactly\; 2\;hits)=5C2*0.95^2*0.05^3$$
$${\left({\frac{{\mathtt{5}}{!}}{{\mathtt{2}}{!}{\mathtt{\,\times\,}}({\mathtt{5}}{\mathtt{\,-\,}}{\mathtt{2}}){!}}}\right)}{\mathtt{\,\times\,}}{{\mathtt{0.95}}}^{{\mathtt{2}}}{\mathtt{\,\times\,}}{{\mathtt{0.05}}}^{{\mathtt{3}}} = {\mathtt{0.001\: \!128\: \!125}}$$
.+118616
$$P(Exactly\; 2\;hits)=5C2*0.95^2*0.05^3$$
$${\left({\frac{{\mathtt{5}}{!}}{{\mathtt{2}}{!}{\mathtt{\,\times\,}}({\mathtt{5}}{\mathtt{\,-\,}}{\mathtt{2}}){!}}}\right)}{\mathtt{\,\times\,}}{{\mathtt{0.95}}}^{{\mathtt{2}}}{\mathtt{\,\times\,}}{{\mathtt{0.05}}}^{{\mathtt{3}}} = {\mathtt{0.001\: \!128\: \!125}}$$
