Question

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 that the two or three rolls will sum to over 15?

Answer 1

probability `=1/18`

Explanation:

If the first two rolls have the same value there are only 2 possibilities for which the sum of the 3 rolls exceeds 15.

#{: (color(black)("roll 1"),color(black)("roll 2"),color(black)("roll 3")), (5, 5, 6), (6,6,6) :}#

Given that the first two rolls are the same:
`color(white)("XX")P("two 5's") = 1/6`
`color(white)("XX")P("two 5's") & P("third roll a 6") = 1/6*1/6 = 1/36`

Similarly
`color(white)("XX")P("two 6's") & P("third roll a 6") = 1/6*1/6 = 1/36`

Since these are disjoint occurrences
`color(white)("XX")P("5-5-6" or "6-6-6")`

`color(white)("XXXXX")=P("5-5-6")+P("6-6-6")`

`color(white)("XXXXX")=2/36 =1/18`