Share

## The Problem of the Points. Two players engage in a game. They are equally matched, and the chances of winning a point are the same for each

Question

The Problem of the Points. Two players engage in a game. They are equally matched, and the chances of winning a point are the same for each player. The first player to score 10 points wins the $100 stakes. The game is interrupted suddenly when Player A has 7 points and Player B has 5 points. How should the stakes be divided fairly

in progress
0

Mathematics
3 years
2021-07-24T04:48:28+00:00
2021-07-24T04:48:28+00:00 1 Answers
9 views
0
## Answers ( )

Answer:Player A receives $77.34375 of the sakes

Player B receives $22.65625 of the stakes

Step-by-step explanation:Given that at the time the game was interrupted, we have;

The number of points player A has = 7 points

The number of points player B has = 5 points

The amount the first player to score 10 points wins = $100

The number of points remaining for player A to win the game = 3

The number of points remaining for player B to win the game = 5

Therefore, the number of trials remaining for a winner to emerge = 3 + 5 – 1 = 7 trials

We take the probability that Player A wins a point as success

We find the likelihood of Plater A winning by using binomial theory as follows;

Therefore, given that the likelihood of Player A winning = 99/128

The stakes should be divided such that Player A gets 99/128 share of the stakes while Player B gets 1 – 99/128 = 29/128 share of the stakes

Therefore, Player A gets (99/128) × $100 = $77.34375

Player B gets (29/128) × $100 = $22.65625