In a lottery,50 tickets are sold,in which 14 | vedclass

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(A) Total number of tickets $= 50$. Number of prize-winning tickets $= 14$. Number of blank tickets $= 50 - 14 = 36$. The man buys $2$ tickets. The to

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$\frac{17}{35}$

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(A) Total number of tickets $= 50$. Number of prize-winning tickets $= 14$. Number of blank tickets $= 50 - 14 = 36$. The man buys $2$ tickets. The total number of ways to choose $2$ tickets from $50$ is ${}^{50}C_2 = \frac{50 	imes 49}{2 	imes 1} = 1225$. The number of ways to choose $2$ tickets such that none of them are prize-winning (both are blank) is ${}^{36}C_2 = \frac{36 	imes 35}{2 	imes 1} = 630$. The probability of not winning any prize is $P(	ext{no prize}) = \frac{630}{1225} = \frac{18}{35}$. The probability of winning at least one prize is $P(	ext{at least one prize}) = 1 - P(	ext{no prize}) = 1 - \frac{18}{35} = \frac{17}{35}$.

In a lottery,$50$ tickets are sold,in which $14$ are prize-winning tickets. If a man buys $2$ tickets,what is the probability that he wins at least one prize?

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