Page 176 - TB_6B

To find out how to share 16 gold coins fairly, you need to find all of the
possible outcomes if the game had continued after De Mere tossed a coin to
get heads on his first try. The tree diagram shows all of the possible outcomes.
H stands for heads, and T stands for tails.

Thteosfsirst Thetosescsond Thteotshsird Winner
H H H De Mere
T De Mere
T
H De Mere
T De Mere's friend

The tree diagram shows that there are 4 possible outcomes if the game had

continued.

The chances of winning for the two people are as follows.

De Mere’s chance of winning = 3
4

De Mere’s friend’s chance of winning = 1
4

So, it would be fair if the two people share the 16 gold coins in proportion to

the chances of winning.

Number of gold coins that De Mere should take = 3 16 =
4

Number of gold coins that De Mere’s friend should take = 1 16 =
4

33. A Fair Game 165