If lottery has 100 numbers and I get to choose 50, what are the odds for hitting it? and what are the odds for hitting atleast 1 number?
The chances of getting the jackpot (all right):
1st ball: 50/100 chance, because there are 50 'right b***s' and 100 b***s in total.
2nd ball: 49/99 chance, because there are 49 'right b***s' and 99 b***s in total.
3rd ball: 48/98 chance, because there are 48 'right b***s' and 98 b***s in total.
...
50th ball: 1/51 chance, because there is 1 'right ball' and 51 b***s in total.
Chance of jackpot=\(\frac{50}{100}*\frac{49}{99}*\frac{48}{98}...*\frac{2}{52}*\frac{1}{51}\)
Which is very close to 0 (Even the calculator gives a 0 as the result, but it's not exactly 0).
The chance of getting at least one ball is 1-(getting no correct numbers)
Getting no correct numbers:
1st ball: 50/100, because there are 50 'wrong b***s' and 100 b***s in total.
2nd ball: 49/99, because there are 49 'wrong b***s' and 99 b***s in total.
...
Wait, this is exactly the same probability to get the jackpot!
Then, (Getting at least 1 ball right)=1-(some number almost close to 0).
So you are almost guaranteed to get at least one ball right... but definitely not a jackpot!
