**Toolbox:**

- Man hitting a target=0.25
- p=\(\large\frac{1}{4}\)
- q=1-\(\large\frac{1}{4}\)=\(\large\frac{3}{4}\)
- The s 7 timesman shoot

P(hits target atleast 2 times)=P(\(x>2\))

=1-P(\(x<2\))=1-[p(x=0)+(x=1)]

=1-[\(C^7_0\)(\(\large\frac{1}{4}\))\(^0\)(\(\large\frac{3}{4})^7\)+\(C^7_1\)(\(\large\frac{1}{4})\;^1\)(\(\large\frac{3}{6})\;^6\)]

=1-[\(\left(\large\frac{3^7}{4^7}\right)\)+7\(\left(\large\frac{3^6}{4^6}\right)\)]

=\(\Large\frac{9094}{16384}\)

=\(\Large\frac{4547}{8152}\)