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 non-prize-winning (blank) tickets = $50 - 14 = 36$.The man buys $2

Vedclass · Accepted Answer

$\frac{17}{35}$

Vedclass · Answer

(A) Total number of tickets = $50$.Number of prize-winning tickets = $14$.Number of non-prize-winning (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 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. $A$ man bought $2$ tickets,then the probability that the man wins at least one prize is:

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