Question

A game has two​ four-sided dice having the numbers 9​, 6​, 3​, and 2 on their...

A game has two​ four-sided dice having the numbers 9​, 6​, 3​, and 2 on their faces. Outcomes in the sample space are pairs such as ​(9​,6​)and ​(2​,2​).

 a. How many elements are in the sample​ space? b. Express the event​ "the total showing is​ even" as a set. c. What is the probability that the total showing is​ even? d. What is the probability that the total showing is greater than 13​?

a)

The sample space is given by:

S = {(9,9), (9,6), (9,3), (9,2), (6,9), (6,6), (6,3), (6,2), (3,9), (3,6), (3,3), (3,2), (2,9), (2,6), (2,3), (2,2)}

So, number of elements in the sample​ space = 16

b)

Let E denote the event 'the total showing is​ even'.

Then,

E = {(9,9), (9,3), (6,6), (6,2), (3,9), (3,3), (2,6), (2,2)}

c)

Required probability =

d)

Let M denote the event 'the total showing is​ even'.

Then,

M = {(9,9), (9,6), (6,9)}

Required probability =

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