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.
In: 1
“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 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
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.
.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%
0.02^10 would be the probability that all ten of your tickets win.
If you want to know the probability that at least one of your tickets wins, it’s much easier to calculate the probability that none of your tickets win and then subtract that from one.
If the probability of a ticket winning is 0.02, then the probability that it loses is 0.98. If you have 10 tickets, the probability that all of them lose is 0.98^10 ~= 0.817.
So if you have ten tickets, the probability that at least one will win is 0.183.
If you take P(win)^attempts, that gives you the probability of winning on every single attempt, which is going to be much lower than the probability of winning one attempt. To find probability of winning at least once over 10 tries it is easier to find the converse (probability of losing every time) and subtract it from 1.
1-((1-0.0002)^10) = 0.0019 or about 2%
Presuming this is a numbers lottery, there’s a special exception- in a numbers lottery, it’s possible for multiple tickets to win, in which case the jackpot is split equally among the winning tickets.
If one of your tickets has the winning number but another person also has the winning number, you only get half the jackpot.
BUT, if you buy all 10 tickets with the same number and there is only one other winner so you take (10/11) * 100% of the jackpot.
If no one else wins, you would take all the jackpot regardless and the other 9 tickets are worthless.
The only reason to put down the same number on multiple tickets would be if you KNEW the lottery outcome ahead of time (cheating) and suspected someone else might also win and you’d take more of a share. This would be very apparent that it is SUPER suspect behavior if you win. Because unless you were cheating and knew this number would win, statistically it is a loss to do this.
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