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Home » The probability of a man hitting a target is . If he fires 7 times, what is the probability of his hitting the target at least twice?
The probability of a man hitting a target is (1 / 4). If he fires 7 times, what is the probability of his hitting the target at least twice?
Binomial Distribution | CBSE | Class 12 | Exercise 32A | Maths | RS Aggarwal
The probability of a man hitting a target is (1 / 4). If he fires 7 times, what is the probability of his hitting the target at least twice?

Using Bernoulli’s Trial we have,
\begin{array}{l} P(\text { Success }=x)={ }^{n} C_{x} \cdot p^{x} \cdot q^{(n-x)} \\ x=0,1,2, \ldots \ldots . n \text { and } q=(1-p), n=7 \\ p= q=? \end{array}
The probability of hitting the target at least twice is =\mathrm{P}(2)+\mathrm{P}(3)+\mathrm{P}(4)+\mathrm{P}(5)+\mathrm{P}(6)+\mathrm{P}(7)
\begin{array}{l} \Rightarrow 1-(\mathrm{P}(0)+\mathrm{P}(1)) \\ \Rightarrow 1-\left({ }^{7} \mathrm{C}_{0}\left(\frac{1}{4}\right)^{0}\left(\frac{3}{4}\right)^{7}+{ }^{7} \mathrm{C}_{1}\left(\frac{1}{4}\right)^{1}\left(\frac{3}{4}\right)^{6}\right) \\ \Rightarrow 1-\left(\frac{10}{4}\right)\left(\left(\frac{3}{4}\right)^{6}\right) \\ \Rightarrow \frac{4547}{8192} \end{array}

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