# confusing probability?

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You are in a lucky draw there is a 0.02% chance that you can win you have 10 tickets. From logic we can say that 0.02 power 10 but should I not have a higher chance of winning the lucky draw can you please explain.

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“0.02 power 10” is probability of win on every ticket. which is indeed very low.

chance of win on at least one ticket is 1-(1-0.0002)^10

(1-0.0002) is chance of loss on one ticket (0.0002 = 0.02%)

(1-0.0002)^10 is chance of loss on every ticket

1-(1-0.0002)^10 is chance of opposite event, i.e. at lest one win.

With low-probability events like yours, you can use 10*0.0002 = 0.2% as an approximation. It is not exact, but it is close enough.

Yes, you should. .02^10 is the chance that all your tickets are winners. Which is, as expected, much lower than the chance of having one single ticket (out of one) win.

What you want is the probability that not all 10 tickets lose.

Does that help?

The better approach is to say you have a .98 chance to lose. With 10 tickets, your chance to lose is .98^10 or .82. If your chance to lose is .82 then your chance to win is .18.

The formula you’re describing is to calculate the probability of winning that same lottery 10 times in a row. So of course it’s really small.

In your case the probability is just 0.02% to win that particular lottery. The actual probability of winning would be:

Number of tickets you have/Number of overall combinations of numbers in the lottery

.0002^10 is the chance you win every ticket.

Your chances of winning a single ticket are 1 minus your chances of losing every ticket

Your chances of LOSING every ticket are .9998^10

So your chances of winning are 1-0.9998^10 = 0.1998% which is very close to 0.2% and should make sense logically with 10 chances at 0.02%