Question

You pay $10 to play the following game of chance. There is a bag containing 12 balls, five are red, three are green and the rest are yellow. You are to draw one ball from the bag.

You will win $14 if you draw a red ball and you will win $12 is you draw a yellow ball.
How much do you expect to win or loss if you play this game 100 times?

I don’t understand what happened to the green balls, how much do you win/lose for them? If I’m supposed to figure it out with the given information, I don’t understand how to. Can somebody please help? Thanks!!

Answer 1

You are expected to win 75 games and lose 25 games.

Explanation:

You do not win anything for drawing a green ball.

5 red

3 green

4 yellow

You only win money for red and yellow balls.

You win money for 5 + 4 = 9 balls or a 9/12 = 3/4 chance of winning.

Playing the game 2 times and winning both is equivalent to:

3/4 * 3/4 = 9/16

This is equivalent to:

(3/4)^n

Where n is the number of times played, this finds the chance that you win all of them.

(3/4)^100

I would ask a teacher or someone, as the wording of the question is rather confusing when it states "How much do you expect to win or lose if you play this game 100 times?".

As far as I know, I don't think you can decide how often you can expect to win or lose. You're guaranteed 3/4 chance for every time played, as nothing changes between games.

However, you are guaranteed 3/4 chance of winning and 1/4 chance of losing for every game. This likely means that you are expected to win 75 games and lose 25 games.