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?

1 Answer
Aug 19, 2016

P("Two sixes") = 1/36

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

Explanation:

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