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

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(C) 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 to

Vedclass · Accepted Answer

$\frac{26}{27}$

Vedclass · Answer

(C) 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 to find the probability of getting at most $2$ successes,i.e.,$P(X \le 2) = P(X=0) + P(X=1) + P(X=2)$.Since the maximum number of successes possible in $2$ trials is $2$,$P(X \le 2)$ covers all possible outcomes.The sum of probabilities of all possible outcomes in a probability distribution is always $1$.Therefore,$P(X \le 2) = 1$.

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 most $2$ successes.

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