# Two players of equal skill A and B are playing a game. They leave off playing (due to some conditions) when A wants 3 points and B wants 2 to win. If prize money is Rs 16,000/-. How can the refree divide the money in a fair way.

### Asked by Sourav | 21st May, 2015, 11:39: AM

Expert Answer:

###
If A and B play 4 more games, the game will be decided. (since if they play less than 4 games , in many cases it remains undecided.)
In any game there are two possibilities: either A wins or B wins.
So total number of cases for 4 games = 2X2X2X2=16
A will be the winner if he wins three or more out of 4.
A can win any three games out of 4 in 4C3 ways. 4C3=4.
A can win all 4 games in 1 way.
Hence, favorable cases for A's win = 4+1=5.
Hence, probability of A's win= 5/16
Hence, probability of B's win = 11/16
Since there chances are in the ratio 5:11, the prize money should also be divided in the same ratio.
Hence A gets 16,000 X 5/(5+11)=5,000
B gets 16,000 X 11/(5+11)=11,000

If A and B play 4 more games, the game will be decided. (since if they play less than 4 games , in many cases it remains undecided.)

In any game there are two possibilities: either A wins or B wins.

So total number of cases for 4 games = 2X2X2X2=16

A will be the winner if he wins three or more out of 4.

A can win any three games out of 4 in 4C3 ways. 4C3=4.

A can win all 4 games in 1 way.

Hence, favorable cases for A's win = 4+1=5.

Hence, probability of A's win= 5/16

Hence, probability of B's win = 11/16

Since there chances are in the ratio 5:11, the prize money should also be divided in the same ratio.

Hence A gets 16,000 X 5/(5+11)=5,000

B gets 16,000 X 11/(5+11)=11,000

### Answered by satyajit samal | 22nd May, 2015, 10:00: AM

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