In a shelf,there are 3 mathematics and 2 phys | vedclass

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(C) Let $X$ be the random variable representing the number of mathematics books selected in $3$ trials.Total number of books = $3 + 2 = 5$.The probabi

Vedclass · Accepted Answer

$\frac{9}{5}$

Vedclass · Answer

(C) Let $X$ be the random variable representing the number of mathematics books selected in $3$ trials.Total number of books = $3 + 2 = 5$.The probability of selecting a mathematics book in a single trial is $p = \frac{3}{5}$.The probability of selecting a physics book is $q = 1 - p = 1 - \frac{3}{5} = \frac{2}{5}$.Since the books are replaced after each selection,the trials are independent,and the random variable $X$ follows a binomial distribution $B(n, p)$ with $n = 3$ and $p = \frac{3}{5}$.The mean of a binomial distribution is given by $E[X] = np$.Substituting the values,we get $E[X] = 3 	imes \frac{3}{5} = \frac{9}{5}$.

In a shelf,there are $3$ mathematics and $2$ physics books. $A$ student takes a book randomly. If he takes a book randomly,successively for $3$ times by replacing the book already taken every time,then the mean of the number of mathematics books,which is treated as a random variable,is:

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