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

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(NONE) The total number of balls is $25$. 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

Vedclass · Accepted Answer

$\frac{7}{27}$

Vedclass · Answer

(NONE) The total number of balls is $25$. 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 $(p)$ $= \frac{13}{25}$.Probability of failure $(q)$ $= 1 - p = 1 - \frac{13}{25} = \frac{12}{25}$.Since $2$ balls are drawn with replacement,this follows a Binomial distribution $B(n, p)$ where $n = 2$.We need the probability of at least $2$ successes,which is $P(X \ge 2) = P(X = 2)$.$P(X = 2) = \binom{2}{2} p^2 q^0 = 1 	imes (\frac{13}{25})^2 	imes 1 = \frac{169}{625}$.

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

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