I'm trying to figure out this question in Logic it states that" imagine that a state lottery pays fair odds. If a ticket costs two dollars and the winner must pick a sequence of five digits, what would the return have to be? How do you decide how to figure out the awnser? (Remember there are over 100,000 different sequences of five digits"
Answers (1)
There are 10^5=100,000 different combinations of 5 digit numbers (00000,00001...99999) and if only the right combination wins there's 1/100000 chance to win. So there's 99,999/100,000 chance to lose the 2 dollars. If the odds are equally good for both, the expected value (Not sure if right word, english isn't my main language) is 0.
1/100000x?+99999/100000x(-2)=0
?=199998
So if the prize is 199,998 dollars then the lottery has equal odds for the gambler and the lottery organizer.
Woops, forgot that you lose the 2 dollars even if you win...
1/100000x(?-2)+99999/100000x(-2)=0
So the right answer is 200,000