Question

If I toss 3 pieces on a tic-tac-toe board at random, and I pay you $9 if the pieces create tic-tac-toe, and you pay me $1 if they don't, do you want to play the game?

A) Yes
B) No

Answer 1

The probability of getting a tic-tac-toe is 2/21. The expected value of the game is -$0.333. Therefore, it is not advisable to play the game.

Step-by-step explanation:

To determine if you should play the game, we can calculate the probability of getting a tic-tac-toe. In a tic-tac-toe board, there are 8 possible ways to get a tic-tac-toe: 3 rows, 3 columns, and 2 diagonals. Since you are tossing 3 pieces randomly, the total number of possible outcomes is 9 choose 3 (or 9C3) which is equal to 84. The probability of getting a tic-tac-toe is then 8/84, which simplifies to 2/21.

Now, let's calculate the expected value. If you win, you receive $9, and if you lose, you pay $1. The expected value can be calculated as follows:

Expected Value = (Probability of Winning * Amount Won) + (Probability of Losing * Amount Lost)

Expected Value = ((2/21) * $9) + ((19/21) * -$1)

Expected Value = -$0.333

Since the expected value is negative, it means that over the long run, you can expect to come out behind in money if you play the game. Therefore, the correct answer is B) No, I expect to come out behind in money.