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Problem 25 on page 55. A pair of fair dice are rolled until a sum of five or seven appears. Find the probability that a five appears
 

Summary: Problem 25 on page 55.
A pair of fair dice are rolled until a sum of five or seven appears. Find the probability that a five appears
first.
Solution One.
Let's first consider one roll of the dice. Let us use T = {1, 2, 3, 4, 5, 6}2
for the sample space. Note that
|T| = 62
= 36. Let
Q(E) =
|E|
|T|
=
|E|
36
whenever E T.
Let Five={(1, 4), (2, 3), (3, 2), (4, 1)}, let Seven={(1, 6, (2, 5), (3, 4), (4, 3), (5, 2), (1, 6)} and let Neither=T
(Five Seven). Thus
Q(Five) =
4
36

  

Source: Allard, William K. - Department of Mathematics, Duke University

 

Collections: Mathematics