SOLUTION: There are 40 golf balls: 10 blue, 16 red, 4 green, 5 yellow, 5 white. Two girls reach into the box and take a ball without looking. If one picks a blue, yellow or white ball, sh

Question 1091677: There are 40 golf balls: 10 blue, 16 red, 4 green, 5 yellow, 5 white. Two girls reach into the box and take a ball without looking. If one picks a blue, yellow or white ball, she wins. If the other picks a red or green, she wins. Is this game fair? Explain.
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

Let's call the two girls GirlA and GirlB

For GirlA to win, she wold need to pick a blue, yellow or white ball. There are 10 blue, 5 yellow and 5 white balls.
Add these values up: 10+5+5 = 20. So there are 20 ways for Girl A to win out of 40 total.

The probability of GirlA winning is 20/40 = 1/2 = 0.5

Keep this value in mind later. Let's call this P = 0.5

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For GirlB to win, she needs to pick a red or green ball. There are 16 red and 4 green balls. They add up to 16+4 = 20. Dividing this value over the grand total (40) gets us 20/40 = 1/2 = 0.5

This probability Q = 0.5 is the same as P = 0.5 as computed above.

Because the two probabilities are the same, this means that either girl has the same chances of winning. Therefore this game is indeed a fair game.

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