You are playing a standard game of tic tac toe with a friend

You are playing a standard game of tic tac toe with a friend. You decide to be O\'s and your friend is X\'s. To win, you must place three of your O\'s in a row. You can win any way (diagonal, across, downward), but you must have 3 O\'s in a row. What is the probability that you will win (i.e. find the probability of placing three of your Os in a row)?

Solution

you have 9 spaces and you need to place 3 O\'s in a row

in total we have = 9C3=84

and our success ways to win we have

8C3 = 56

there are 8 rows ( 3 across, 3 downward, 2 diagonal)

probability = 56/ 84 = 0.67