A person buys a lottery ticket in 50 lotteries, in each of which his chance of winning a prize is `1/(100)` . What is the probability that he will win a prize (a) at least once (b) exactly once (c) at least twice?

Explanation

Let `X` represent the number of winning prizes in `50` lotteries. The trials are Bernoulli trials.

Clearly, `X` has a binomial distribution with `n=50 and p=1 / 100`

`therefore q=1-p=1-frac{1}{100}=frac{99}{100} `

`therefore {P}({X}=x)=^{n} {C}_{x} q^{n-x} p^{?}=^{50} {C}_{x}(frac{99}{100})^{50-x} cdot(frac{1}{100})^{x}`

(a) `P (`winning at least once)` =P(X geq 1)`

`=1-P(X<1)`

`=1-P(X=0) `

`=1-^{30} C_{0}(frac{99}{100})^{50} `

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