Question

In the game of tic-tac-toe, if all moves are performed randomly the probability that the game will end in a draw is . Suppose ten random games of tic-tac-toe are played. What is the probability that at least one of them will end in a draw?

Answer 1

0.7429 (With an assumed draw probability of 0.127 per match)

Explanation:

After searching up online, it seems that the probability for a draw in a tic tac toe game is 0.127

Since this question is incomplete without this probability stated, let's assume this is what the question HAD stated.

Now, to find the probability that at least one of 10 games ends in a draw, we must simply compute that no tic tac toe game end in a draw, and subtract that from the total probability of 1.

This becomes:

Probability of at least one game being a draw = 1 - probability of no games being a draw

For 10 games to NOT be a draw, we multiply the chance of no draw 10 times over. This is:

1 - 0.127 = 0.873 (probability of no draw in a single game)

0.873^10 = 0.2571 (probability of no draw in 10 games)

1 - 0.2571 = 0.7429 (probability of at least one draw in 10 games)

The probability assumed at the start may be changed according to the question, and the solution method repeated to get the required answers.