Question

In a gambling game, a player is paid Php 10 if he draws a jack or a queen and Php 15 if he draws a king or an ace from an ordinary deck of 52 playing cards. If draws any other card, he losses. How much should he pay to play if the game is fair?​

Answer 1

Given : a player is paid Php 10 if he draws a jack or a queen and Php 15 if he draws a king or an ace from an ordinary deck of 52 playing cards. If draws any other card, he losses.

To Find : :How much should he pay to play if the game is fair

Solution:

total 52 cards

4 jack  , 4 queen , 4 king 4 aces

Probability draw a jack or a queen = 8/52  = 2/13

Probability draw a  king or an ace  = 8/52   = 2/13

draws any other card  =   (52 - 8 - 8 ) /52  = 36/52   = 9/13

X           P(X)            X.P(X)

10          2/13          20/13

15          2/13           30/13

0          9/13          -9P/13

20/13  + 30/13  + 0(9/13)

=  50/13

Chances of winning = 50/13

Hence  he pay to play if the game  = 50/13  for game to be fair

=  3.85 P

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