A person buys a lottery ticket in 50 lotterie | vedclass

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Question

(A) Let $X$ represent the number of winning prizes in $50$ lotteries. The trials are Bernoulli trials. Clearly,$X$ follows a binomial distribution wit

Vedclass · Accepted Answer

$1 - (\frac{99}{100})^{50}$

Vedclass · Answer

(A) Let $X$ represent the number of winning prizes in $50$ lotteries. The trials are Bernoulli trials. Clearly,$X$ follows a binomial distribution with $n = 50$ and $p = \frac{1}{100}$.$	herefore q = 1 - p = 1 - \frac{1}{100} = \frac{99}{100}$.$	herefore P(X = x) = ^{n}C_{x} q^{n-x} p^{x} = ^{50}C_{x} (\frac{99}{100})^{50-x} \cdot (\frac{1}{100})^{x}$.$P(	ext{winning at least once}) = P(X \geq 1)$.$= 1 - P(X $= 1 - P(X = 0)$.$= 1 - ^{50}C_{0} (\frac{99}{100})^{50}$.$= 1 - 1 \cdot (\frac{99}{100})^{50}$.$= 1 - (\frac{99}{100})^{50}$.

$A$ person buys a lottery ticket in $50$ lotteries,in each of which his chance of winning a prize is $\frac{1}{100}$. What is the probability that he will win a prize at least once?

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