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

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(C) Total balls $= 25$. Odd numbers are ${1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25}$,which are $13$ in total. Probability of success $(p)$ $= \fr

Vedclass · Accepted Answer

$\frac{481}{625}$

Vedclass · Answer

(C) Total balls $= 25$. Odd numbers 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,the probability of getting no success in $2$ trials is $q 	imes q = \left(\frac{12}{25}ight)^2 = \frac{144}{625}$. The probability of getting at least one success $= 1 - P(	ext{no success}) = 1 - \frac{144}{625} = \frac{625 - 144}{625} = \frac{481}{625}$.

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 at least one success.

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