Megabucks is a lottery game played in most states . A random drawing of 6 number

Question

Megabucks is a lottery game played in most states . A random drawing of 6 numbers out of all 36 numbers from 1 to 36 is made. To win the jackpot (which is usually worth several million dollars) a ticket should have correct all the 6 numbers drawn regardless of their order. (A filled ticket contains 6 numbers.) What is the probability that a randomly filled ticket wins the jackpot?

A player who correctly chooses (exactly) five out of the six winning numbers gets a smaller prize. What is the probability of winning this small prize?

Explanation / Answer

Number of ways of selecting 6 numbers out of 36 numbers is

C(36,6) = 1947792

Out of these possible combination only one is for jackpot so

P(jackpot) = 1 / 1947792 = 0.0000005134

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Number of ways of choosing 5 numbers out of 6 seleected numbers and rest 1 number out of remaining 30 numbers is

C(6,5) * 30 = 180

So the probability of winning this small prize is

P(small prize) = 180 / 1947792 = 0.0000924

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