Question

A game between two equally skilled players is ended before a winner is declared. Player A needs 3 more points to win, and player B needs 2 more points to win. How should the stakes be divided between the two players? Blaise Pascal used the Arithmetical Triangle to solve this problem. In the division of the stakes, what is the ratio of player A's winnings to Player B's winnings?

Answer 1

Answer: player A = 11/16 and player B = 5/16

Step-by-step explanation:

If a coin was to be tossed to determine the winner possible outcomes using arithmetical triangle.

Player A needs 2 points = 11

Player B needs 3 points = 5

Total outcome of tossing a coin = 16

Player A = 11/16 = 0.6875

Player B = 5/16 = 0. 3125

Or

Using the fifth roll of the pascal triangle (2+3) outcome

( 1, 4, 6, 4, 1 )

Addition of the first 3 represent Player A chances of winning = ( 1+ 4 + 6 ) = 11

And the last two = ( 1 + 4 ) = 5 represents the chances of team B winning

Total number of outcome = ( 1 + 4 + 6 + 4 + 1 ) = 16