Question

There are 10 cards placed face down on a table. Four of the cards have stars on them and the other 6 are blank. You win if you draw a card with a star. How can the game be made fair? The game is already fair. Add 2 cards with stars. Add a star to 1 of the blank cards. Take away 2 blank cards. win if you draw a card with a star. How can the game be made fair?

Answer 1

In the original game, the probability of winning is 4/10 or 2/5. To make the game fair, we want to adjust the number of star cards and blank cards so that the probability of winning is 1/2 or 5/10.

Option 1: Add 2 cards with stars.

If we add 2 cards with stars, we will have a total of 12 cards, 6 of which will have stars. The probability of winning will be 6/12 or 1/2, making the game fair.

Option 2: Add a star to 1 of the blank cards.

If we add a star to 1 of the blank cards, we will have a total of 11 cards, 5 of which will have stars. The probability of winning will be 5/11, which is not exactly 1/2 but is very close. This option is a good approximation of a fair game, but not perfect.

Option 3: Take away 2 blank cards.

If we take away 2 blank cards, we will have a total of 8 cards, 4 of which will have stars. The probability of winning will be 4/8 or 1/2, making the game fair.

Therefore, options 1 and 3 will make the game fair, while option 2 is a good approximation of a fair game.