Aperson in a casino decides to play blackjack until he loses a game, but he will not play more than 3 games. let l denote a loss and w denote a win. what is the sample space for this random experiment

L=loss, W=win

The sample space is the set of all possible outcomes, so the set of all possible scenarios in the experiment.

what may happen is the following:

W, W, W
(win, win, win, then stop because the player wont play more than 3 games) 

W, W, L

W, L 
(loses the second game and stops)

L
(loses the first game and stops)

{WWW, WWL, WL, L}

21:10, 21/10, 21 to 10.(Siimplified: 10.5:5, 10.5 to 5, 10.5/5)
Hope this helps