In a lottery,16 tickets are sold and 4 prizes | vedclass

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(B) The probability of winning a prize with a single ticket is $p = \frac{4}{16} = \frac{1}{4}$.The probability of not winning a prize with a single t

Vedclass · Accepted Answer

$\frac{175}{256}$

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(B) The probability of winning a prize with a single ticket is $p = \frac{4}{16} = \frac{1}{4}$.The probability of not winning a prize with a single ticket is $q = 1 - p = 1 - \frac{1}{4} = \frac{3}{4}$.For $n = 4$ tickets,the probability of winning at least one prize is $1 - P(	ext{winning zero prizes})$.$P(	ext{winning zero prizes}) = q^4 = \left(\frac{3}{4}ight)^4 = \frac{81}{256}$.Therefore,the probability of winning at least one prize is $1 - \frac{81}{256} = \frac{256 - 81}{256} = \frac{175}{256}$.

In a lottery,$16$ tickets are sold and $4$ prizes are awarded. If a person buys $4$ tickets,what is the probability of winning at least one prize?

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