SOLUTION: Suppose that the probability of winning the lottery is one in a million. If you play the lottery every day for 50 years(50*365=18,250 days), what is the probability that you win th

Question 1075541: Suppose that the probability of winning the lottery is one in a million. If you play the lottery every day for 50 years(50*365=18,250 days), what is the probability that you win the lottery at least once?
I am so lost any help i'd be grateful for.
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
It becomes a Poisson with np, where n=18250 and p=0.000001. You use a Poisson where n goes to infinity, p goes to 0, but np is NOT 0.
The parameter is 0.01825
Want the probability of NOT winning it and subtract it from 1
That probability is e^(-0,01825)=0.9819. The other parts of the Poisson formula are 1, so they are ignored.
Therefore, the probability of winning is 1-0.9819=0.0091.
This is why one can predict number of winners in a lottery where 330 million tickets are sold and the probability of winning is 1 in 110 million. np=3 and the distribution of winners and their probabilities can be taken from a table or a calculator easily.
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