# If two dice are rolled once and one die rolled a second time if the first two rolls have same number, what is the probability of getting a sum of 14?

Nov 7, 2015

Work backwards, then determine the probabilities

#### Explanation:

If the sum is 14, then possible values for the second roll (given that the first two are equal) and the value of the first rolls:

(First double, Second single)
(6-6,2)
(5-5,4)
(4-4,6)

P(two 6's then a 2) $= {\left(\frac{1}{6}\right)}^{3} = \frac{1}{216}$

Same probability for the other two outcomes.

Total probability $= \frac{3}{216} = \frac{1}{72}$

hope that helped