Question

For a certain game, three numbers are drawn, each from 1 to 10. A player can win if the product of his or her three numbers is odd. Initially, the same number may be picked up to three times. Later, the rules are changed so that each number may only be picked once. Approximately how much does this reduce a person's probability of winning?

Answer 1

Explanation:

if you can pick the same card 3 times the probability of winning is

`((5)/(10))^(3) = (1)/(8)`

but if you remove each card after you've picked them it's :

`(5)/(10).(4)/(9).(3)/(8)= (60)/(720)`

notice if you remove an odd card every time you pick one of them you are also removing one of the overall cards

and if you subtract these two you get :
`(1)/(8) - (60)/(720) =0.0417`

which is like 4 percent