$\begin{array}{1 1}(A)\;^5C_4(0.7)^4(0.3) & (B)\;^5C_1(0.7)(0.3)^4\\(C)\;^5C_4(0.7)(0.3) & (D)\;(0.7)^4(0.3)\end{array} $

- A random variable $X$ taking values $0,1,2,\dots ,n$ has bianomial distribution with parameters $n$ and $p$, its probability distribution is given by
- $p(X=r)=c^{n}_{r} p^{r}q^{n-r}$
- When $q=1-p; r=0,1,2,\dots,n$

If the probability a person is not a swimmer is $0.3$ then the probability a person is a swimmer

$p=1-0.3$

=$0.7$

$q=1-p=0.3$

Probability that out of $5$ persons $4$ are swimmers

=$p(X=4)$

=$c^{5}_{4}(0.7)^{4}(0.3)^{5-4}$

=$c^{5}_{4}(0.7)^{4}(0.3)$

Hence $'A'$ option is correct

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