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 six random games of tic-tac-toe are played. What is the probability that at least one of them will end in a draw?

Question

Matthew Mooney

Mathematics

30 March, 07:28

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 six random games of tic-tac-toe are played. What is the probability that at least one of them will end in a draw?

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Elisha Jacobs · Answer 1

Completed 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 0.127. Suppose six random games of tic-tac-toe are played. What is the probability that at least one of them will end in a draw?

Answer:

0.557

Step-by-step explanation:

For each game, the probability of not end in a draw is 1 - 0.127 = 0.873. Thus, because each game is independent of each other, the probability of all of them not end in a draw is the multiplication of the probability of each one:

0.873x0.873x0.873x ... x0.873 = 0.873⁶ = 0.443

Thus, the probability that at least one of them end in a draw is the total probability (1) less the probability that none of them en in a draw:

1 - 0.443

0.557