Question

A single fair die is rolled twice. Construct a tree diagram and determine the probability that: a) a double (for example 1, 1 or 2, 2, etc.) is rolled. b) a sum of 8 is rolled. c) a sum of 2 is rolled.

Answer 1

Answer:

Tree diagram will be like

Total outcomes of fair dice rolled twice are

(1,1)	(1,2)	(1,3)	(1,4)	(1,5)	(1,6)
(2,1)	(2,2)	(2,3)	(2,4)	(2,5)	(2,6)
(3,1)	(3,2)	(3,3)	(3,4)	(3,5)	(3,6)
(4,1)	(4,2)	(4,3)	(4,4)	(4,5)	(4,6)
(5,1)	(5,2)	(5,3)	(5,4)	(5,5)	(5,6)
(6,1)	(6,2)	(6,3)	(6,4)	(6,5)	(6,6)

therefore n = 36

Now

a) here event is double is rolled. hence number of outcomes this event are

(1,1)

(2,2)

(3,3)

(4,4)

(5,5)

(6,6)

We know that probability of an event is (Number of favorable outcomes) / ( Total number of possible outcome )

hence probability for a) is 6/36.

b) event is sum 8 . outcome are

(2,6)

(3,5)

(4,4)

(5,3)

(6,2)

hence probability for b) is 5/36.

c) here event is sum 2. outcomes are

(1,1)

hence probability for c) is 1/36.