Question

Question 1: Roll two fair dice. Then the sample space S is the following.
S =
(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)

Let E be the event that the sum of the dice is odd, let F be the event that the first die lands on 1,
and let G be the event that the sum is 5.
Describe the following events:
(a) EF,
(b) E ∪ F,
(c) FG,
(d) EF^c, and
(e) EFG.
You may either explicitly list the outcomes in the event, or give a concise description of all the
outcomes in the event.

Answer 1

a)EF is the event that first die lands on 1 and sum of die is odd

events under EF ={ (1,2), (1,4) ,(1,6) }

b)

EF is the event that first die lands on 1 or sum of die is odd or both

events under E U F ={ (1,1) (1,2) (1,3) (1,4) (1,5) (1,6),(2,1) ,(2,3) (2,5) (3,2) (3,4) (3,6) (4,1) (4,3) (4,5) (5,2) (5,4) (5,6) (6,1) (6,3) (6,5)

c)

FG is the outcome where first die lands on 1 and sum of dies is 5

events under FG ={ (1,4) }

d)

EF^c is the outcome where first die lands on other and 1 and sum of dies is odd

events under EF^c ={ (2,1) ,(2,3) (2,5) (3,2) (3,4) (3,6) (4,1) (4,3) (4,5) (5,2) (5,4) (5,6) (6,1) (6,3) (6,5) }

e)

EFG is the outcome of having 1st die as 1 , sum is odd and sum is 5,

events under EFG ={ (1,4) }