Many thanks !

"idiots guide to probability"

There's a lot of other stuff there too, but you should find the info. you want.

Thankyou

sfwc
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"I know that entering the lottery ( which has a stated probability of 1 in 14 million of winning the jackpot) every week for 20 years dose not significantly increas your chances of winning it, over some on who enters just once.
How ever if you do enter 1X52X20 times how do you calculate how much more likely you are to win?
Conversly
If you enter 1040 times on the one draw how much more likely are you to win than the dedicated weekly player?
Is it'simply 1040 divided by 14 million ( ie 1 in 14,000) or
is it calculated using a sequence like (1 / (14,000,000)) (1 / (14,000,000 - 1)) (1/13,999,998)etc.
if so is there a quick way of evaluating the sequence?"

Suppose that a person enters your jackpot once a week for 20 years. then the probability that the person misses each week is 1-1/14,000,000. The probability that they miss 1040 times in a row is (1 - 1/14,000,000)^1040. Now 1-x is very close to e^x, so this number is very close to e^{-1040/14,000,000}. From Taylor series, we know that e^x is approximately 1 + x + x^2 /2 + x^3/6 + ..., so this number is about 1 - 1040/14,000,000 + (1040/14000000)^2 / 2. So the chance of winning the lottery is about 1040/14000000 - (1040/14000000)^2/2.

This second correction term is very small, so doesn't affect the answer much.

Now the person who plays 1040 different numbers on the same lottery has exactly a 1040 / 14000000 chance of winning, since it is just 1/14000000 added up 1040 times. So the chance of winning is about (1040/14000000)^2/2 lower for the first method than the second. Not much of a difference.

Mark