If you buy a lottery ticket in 50 lotteries, in each of which your chance of winning a prize is 1/100, what is the (approximate) probability that you will win a prize

# If you buy a lottery ticket in 50 lotteries, in each of which your chance of winning a prize is 1/100, what is the (approximate) probability that you will win a prize

H
Asked by 2 years ago
240 points

If you buy a lottery ticket in 50 lotteries, in each of which your chance of winning a prize is 1/100, what is the (approximate) probability that you will win a prize
(a) at least once?
(b) exactly once?
(c) at least twice?

If you
hansel

Answered by 2 years ago
8.7k points

Under these circumstances we use a Poisson distribution

$$P(X=k)=\frac{\lambda^k e^{-\lambda}}{k!}$$

with

$$\lambda=n\times p=50\times(1/100)=0.5$$

part (a)

$$P(\text{at least once})=1-P(\text{not winning})$$

$$=1-\frac{0.5^0e^{-0.5}}{0!}\approx 0.3935$$

part (b)

$$P(\text{exactly once})=\frac{0.5^1e^{-0.5}}{1!}=0.3033$$

part (c)

using info from parts (a) and (b),

$$P(\text{at least twice})=1-P(\text{not winning or exactly once})$$

$$1-0.3935-0.3033=0.3032$$

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