Theoretical Probability

Theoretical Probability

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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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