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13 September, 20:28

In a board game, you must roll two 6-sided number cubes. You can only start the game if you roll a 3 on at least one of the number cubes. Suppose you rolled the two number cubes 100 times, would you expect at least one 3 more or less than 34 times? Explain.

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  1. 13 September, 20:35
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    The odds of rolling a 3 on a 6-sided number cube is 1 out of 6. The odds of rolling a 3 on either of two 6-sided cubes are 1/3. This is because 1/6 * 2 = 1/3. Therefore, an average of one-third of rolls will have a 3 in them. 1/3 expressed as a decimal is. 3 repeating (.3333333 etc) and that rounds to 33 which is less than 34.

    Therefore, the answer is less than 34 and the explanation is above.
  2. 13 September, 20:56
    0
    Prob (at least one 3) = 1 - Prob (no 3 in both dices)

    Prob (no 3 in 1 dice) = 5/6

    Prob (no 3 in both dices) = 5/6x5/6 = 25/36

    so Prob (at least one 3) = 1 - 25/36 = 11/36

    in 100 rolls, the expected rolls w at least one 3 is 100 x 11/36 = 30.56

    i. e. less than 34 times
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