Probability of A winning the game

In summary, A and B play a game with probabilities of A winning, B winning, or a draw. The winner of the first non-draw game is declared the overall winner. To compute the probability of A winning at game n, we can calculate P(A wins) by adding the probabilities of A winning in each individual game. To find P(A,n), we can use the formula P(A wins)P(A,n) = P(draw in first n-1 games) * P( A wins in nth game | draw in first n-1 games). It is recommended to clearly lay out the sample space to solve this problem.
  • #1
TomJerry
50
0
Suppose A and B play over and over , independently a game which each time results in either a win for A , a win for B or draw (meaning no decision) with probabilities P(A), P(B) and P(D). Suppose they keep playing until the first game that does not result in a draw , and call the winner of that game the overall winner. Compute
i) P(A wins at game n)
ii) P(a wins)
 
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  • #2
P(A,n) = P(draw in first n-1 games) * P( A wins in nth game | draw in first n-1 games)

P(A wins) = P(A wins first game) + P(A wins second game) + ...

This seems like it belongs to the homework guidance forum though
 
  • #3
I think laying out clearly the sample space should take you around 90% towards
the answer.
 

1. What is the definition of probability in the context of a game?

Probability is the measure of how likely it is for a certain event to occur. In the context of a game, it refers to the chances of a player or team winning.

2. How is the probability of A winning the game calculated?

The probability of A winning the game is calculated by dividing the number of favorable outcomes (A winning) by the total number of possible outcomes.

3. What factors can affect the probability of A winning the game?

The probability of A winning the game can be affected by various factors such as the skills and abilities of both teams/players, the rules of the game, and any external factors such as weather conditions.

4. Is probability a guarantee that A will win the game?

No, probability does not guarantee that A will win the game. It is simply a measure of the likelihood of A winning based on the given circumstances.

5. How can understanding probability help in predicting the outcome of a game?

Understanding probability can help in predicting the outcome of a game by providing a basis for decision-making and strategy. By knowing the probability of A winning, players or teams can adjust their tactics and make more informed decisions during the game.

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