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 Aaron 2 years ago

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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Asked: 2 years ago