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The results are in, and the winners for MMM #10 Sameer Shah! Thanks to everyone who participated once again.

The Answer

Here is Sameer’s explanation:

So the probability that a member of the Quach family does not win the lottery in 25 years is 32/243. Since winning each year is independent of any other year, we know:

P(not winning any year)=P(not winning 1st year)*P(not winning 2nd year)*…*P(not winning 25th year)

And since the probability of not winning each year is the same, we get:

P(not winning any year)=P(not winning in nth year)^25
32/243=P(not winning in nth year)^25
P(not winning in nth year)=(32/243)^(1/25)

Now we need to find the probability of winning at least once in a five year interval, which is actually 1-P(not winning in 5 year interval).

P(not winning in 5 year interval)=P(not winning in 1st year)*P(not winning in 2nd year)*…*P(not winning in 5th year)

P(not winning in 5 year interval)=P(not winning in nth year)^5

P(not winning in 5 year interval)=(32/243)^(1/5)=2/3

Since we want to find P(winning in 5 year interval), we know that that will have to be 1/3.

I want me some of them odds.