An urn contains 25 balls numbered 1 to 25. Su | vedclass

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(C) Total balls $= 25$. The odd numbers between $1$ and $25$ are ${1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25}$,which are $13$ in total.Probability

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$169/625$

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(C) Total balls $= 25$. The odd numbers between $1$ and $25$ are ${1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25}$,which are $13$ in total.Probability of success $(p)$ $= 13/25$.Probability of failure $(q)$ $= 1 - p = 1 - 13/25 = 12/25$.Since $2$ balls are drawn with replacement,this follows a binomial distribution $B(n, p)$ with $n = 2$.The probability of getting exactly $2$ successes is given by $P(X = 2) = ^nC_r \cdot p^r \cdot q^{n-r}$.Here,$n = 2$ and $r = 2$.$P(X = 2) = ^2C_2 \cdot (13/25)^2 \cdot (12/25)^0 = 1 \cdot (169/625) \cdot 1 = 169/625$.

An urn contains $25$ balls numbered $1$ to $25$. Suppose an odd number is considered a 'success'. $2$ balls are drawn from the urn with replacement. Find the probability of getting exactly $2$ successes.

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