Answer to Question #16030 in Statistics and Probability for Vlatko

Question #16030

A Lottery consists of 200 lottery tickets. There are 30 tickets with some prize and only three of them with the grand prize. Alex bought 10 tickets. Find the probability that he won at least one grand prize if he won 5 prizes.

Thanks a lot!

Expert's answer

The matter of this problem is to determine the essential conditions. They are that 3 of 30 prize tickets are with the grand prize and that Alex won 5 prizes. Other given conditions are excess.

We can choose 5 prize tickets (maybe with grand prizes) from 30 prize tickets in a C(30,5) ways and we can choose 5 prize tickets without grand prize in C(30-3,5) = C(27,5) ways. Therefore,

P(no grand prize in 5 prize tickets) = C(27,5)/C(30,5) = 115/203.

P(at least 1 grand in 5 prize) = 1 - P(no grand in 5 prize) = 1 - 115/203 = 88/203.

So, probability that he won at least one grand prize if he won 5 prizes is 88/203.