(Probability) To win the California Mega Millions lottery, one must correctly pick five (distinct) lucky .....?

Question

To win the Mega Millions lottery, one must correctly pick five (distinct) lucky numbers (integers) from 1 to 75 and one MEGA number (integer) from 1 to 15 on a MEGA Millions play slip. Since each collection is equally likely, the probability that a particular set of 5 distinct numbers plus a Mega number wins in a given week is

look at formula above^^^^

Suppose that you buy one ticket each week for $1 until you win a Mega Millions.

(a) What is the probability that you will win a Mega Millions within a particular calendar year?

(b) Assume that you work for exactly 30 years before you retire and that you buy one ticket each week, what is the probability that you will win a Mega Millions before you retire?

Answer 1

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a) assuming 52 weeks in a year, the prob. that you dont win is (1-p)^52=.999999799;

so prob that you win is 1-p=.000000201.

b) assuming 30x52=1560 weeks, prob. that you dont win is (1-p)^1560=.999993975;

so prob. that you win is 1-p=.000006025