Question

A 6-sided die rolled twice. Let E be the event "the first roll is a 1" and F the event "the second roll is a 1".

1. Find the probability of showing a 1 on both rolls. Write your answer as a reduced fraction.

Answer 1

The sample space on rolling two dice is given by:

(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)

There are a total of 36 outcomes possible. Out of those 36 outcomes, there is only one outcome of showing a 1 on both rolls. Hence,

P(Showing a 1 on both rolls)

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