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I have two bags with marbles inside. Bag A is blue and bag B is red. Bag A contains 3 marbles. On red, one blue, and one green. Bag B contains 2 marbles - one red and one blue.
To play the game you have to draw one marble from each bag without looking. If both the marbles you draw are the same you win a prize.
The theoretical probability of winning a prize is 2/6 or 1/3. This is because there are 6 possibilities of the kinds of marbles you draw. To win there are 2 possibilities out of 6. Those possibilities are picking one red and another from bag A and B and picking 2 blue marbles from each bag.
Now, lets say we play 30 rounds. An you win 9 times out of 30 games. How do the results in these games compare to the theoretical probability?
The theoretical probability of winning out of 30 games is 10/30. But what actually happened is that you won 9/30 times. You won one less than the theoretical probability.
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