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?

Explanation

Given that, man shoots `7` times, `n=7`

Probability of hitting target `p=0.25=frac{1}{4}`

`q=1-p=1-frac{1}{4}=frac{3}{4}, r ge 2`

Where `P(X)=^nC_r (p)^r (q)^(n-r)`


`therefore P(r ge 2)=1-[P(r=0)+P(r=1)]`

`Rightarrow 1-[^7C_0 (frac{1}{4})^0 (frac{3}{4)^(7-0)+^7C_1 (frac{1}{4})^1 (frac{3}{4)^(7-1)]`

`Rightarrow 1-[(frac{3}{4)^(7)+7(frac{1}{4})^1 (frac{3}{4})^(6)]`

`Rightarrow 1-[(frac{3}{4})^(6)[frac{3}{4}+frac{7}{4}])]`

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