# The probability of a man hitting a target is 0.25.He shoots 7 times.What is the probability of his hitting at least twice?

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• 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$$\left(\large\frac{3^6}{4^6}\right)$$]
=$$\Large\frac{9094}{16384}$$
=$$\Large\frac{4547}{8152}$$

edited Mar 16, 2013