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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.

Respuesta :

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.
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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