# if one person plays a game and their chances of winning are 6 over 16 and then 400 people play how many people would you expect to win. how would I do this.

zach9414 | Certified Educator

So in this problem the chances of someone winning the game is 6 out of every 16. This could also be written as `6/16`

This is just telling us that for every 16 people who play the game, we should expect there to be 6 winners. So we can actually set up a multiplication problem for this:

`16*(6/16)=6`  This is showing us that if we have 16 people playing, and the chances of winning are 6 out of every 16, then result should be 6 winners when we multiply this. Similarly if we have twice as many people play (32 players) then we can set up a similar equation:

`32*(6/16)=12`  This is showing us that if we have 32 people playing this game, and the chances are still the same, then the result should be 12 winners of this game.

Lastly, if we know that there are 400 players, then we can still set up the same equation with the same chances, and it should result in the total number of expected winners:

`400*(6/16)=150`

So if we have 400 people playing this game, and the chances of winning are still 6 out of every 16 people, then the total number of expected winners should be 150 people.