Consider a lottery that sells $n^{2}$ tickets and awards $n$ prizes. If one buys $n$ tickets the probability of his winning is i.e., getting at least one prize is

\frac{n}{n_{C_{n}}^{2}}

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1 - \frac{^{(n^{2} - n)} C_{n}}{n_{C_{n}}^{2}}

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\frac{(n^{2} - n)}{n^{2}}

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\frac{1}{n_{C_{n}}^{2}}

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Solution

The correct option is B $1 - \frac{^{(n^{2} - n)} C_{n}}{n_{C_{n}}^{2}}$
Probability that on buying $n$ tickets, the man gets no prize = $\frac{_{n}^{(n^{2} - n)} C}{_{n}^{n^{2}} C}$
Hence, required probability = $1 - \frac{_{n}^{(n^{2} - n)} C}{_{n}^{n^{2}} C}$ .
Hence, (b) is correct.

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Consider a lottery that sells n2 tickets and awards n prizes. If one buys n tickets the probability of his winning is i.e., getting at least one prize is

The correct option is B 1−(n2−n)Cnn2CnProbability that on buying n tickets, the man gets no prize = (n2−n)nCn2nCHence, required probability = 1−(n2−n)nCn2nC.Hence, (b) is correct.

Consider a lottery that sells $n^{2}$ tickets and awards $n$ prizes. If one buys $n$ tickets the probability of his winning is i.e., getting at least one prize is

The correct option is B $1 - \frac{^{(n^{2} - n)} C_{n}}{n_{C_{n}}^{2}}$
Probability that on buying $n$ tickets, the man gets no prize = $\frac{_{n}^{(n^{2} - n)} C}{_{n}^{n^{2}} C}$
Hence, required probability = $1 - \frac{_{n}^{(n^{2} - n)} C}{_{n}^{n^{2}} C}$ .
Hence, (b) is correct.