Julie throws a fair red dice once and a fair blue dice once. How do you calculate the probability that Julie gets a six on both the red dice and blue dice. Secondly, calculate the probability that Julie gets at least one six?

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Answer 1 · 2016-08-19T15:59:15

#P("Two sixes") = 1/36#

#P("At least one six") = 11/36#

Probability of getting a six when you roll a fair die is #1/6#. The multiplication rule for independent events A and B is

#P(AnnB) = P(A)*P(B)#

For the first case, event A is getting a six on the red die and event B is getting a six on the blue die.

#P(AnnB) = 1/6*1/6 = 1/36#

For the second case, we first want to consider the probability of getting no sixes.

The probability of a single die not rolling a six is obviously #5/6# so using multiplication rule:

#P(AnnB) = 5/6*5/6 = 25/36#

We know that if we add up the probabilities of all the possible outcomes we will get 1, so

#P("At least one six") = 1 - P("No sixes")#

#P("At least one six") = 1 - 25/36 = 11/36#