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Home » A man can hit a bird, once in 3 shots. On this assumption he fires 3 shots. What is the chance that at least one bird is hit?
A man can hit a bird, once in 3 shots. On this assumption he fires 3 shots. What is the chance that at least one bird is hit?
Binomial Distribution | CBSE | Class 12 | Exercise 32A | Maths | RS Aggarwal
A man can hit a bird, once in 3 shots. On this assumption he fires 3 shots. What is the chance that at least one bird is hit?

The probability that the bird will be shot, is 1 / 3
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=3 \\ p=1 / 3 q=2 / 3 \end{array}
Probability that he will hit at least one bird is =
\begin{array}{l} P(1)+P(2)+P(3) \\ \Rightarrow{ }^{3} C_{1}\left(\frac{1}{3}\right)^{1}\left(\frac{2}{3}\right)^{2}+{ }^{3} C_{2}\left(\frac{1}{3}\right)^{2}\left(\frac{2}{3}\right)^{1}+{ }^{3} C_{3}\left(\frac{1}{3}\right)^{3}\left(\frac{2}{3}\right)^{0} \Rightarrow \frac{19}{27} \end{array}

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