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# The probability that a person is not swimmer is 0.3.The probability that out of 5 persons 4 are swimmers is

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

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A)
Toolbox:
• 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