In a certain lottery,10,000 tickets are sold | vedclass

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Question

(A) Total number of tickets $= 10,000$. Number of prize-winning tickets $= 10$. Number of non-prize-winning tickets $= 10,000 - 10 = 9,990$. We buy $1

Vedclass · Accepted Answer

$\frac{^{9990}C_{10}}{^{10000}C_{10}}$

Vedclass · Answer

(A) Total number of tickets $= 10,000$. Number of prize-winning tickets $= 10$. Number of non-prize-winning tickets $= 10,000 - 10 = 9,990$. We buy $10$ tickets. The total number of ways to choose $10$ tickets out of $10,000$ is $^{10000}C_{10}$. The number of ways to choose $10$ tickets such that none of them are prize-winning is choosing $10$ tickets from the $9,990$ non-prize-winning tickets,which is $^{9990}C_{10}$. Therefore,the probability of not getting a prize is $P = \frac{^{9990}C_{10}}{^{10000}C_{10}}$.

In a certain lottery,$10,000$ tickets are sold and $10$ equal prizes are awarded. What is the probability of not getting a prize if you buy $10$ tickets?

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