Answer to Question #211326 in Discrete Mathematics for Naresh

Question

A fair six-sided dice is thrown and the scores are noted.

Event X: The total of the two scores is 4.

Even Y: The first score is 2 or 5.

a)              Construct the table by showing the sample spaces.                                          

                                                                     

Answer 1

A dice is thrown two times. So, total outcomes = $6^2=36.$

Event X: The total of the two scores is 4.

Sample space for X = $(1,3), (2,2), (3,1)$

Event Y: The first score is 2 or 5

Sample space for Y =$(2,1), (2,2), (2,3),(2,4), (2,5), (2,6),(5,1), (5,2), (5,3),$

$(5,4), (5,5), (5,6)$

$$\def\arraystretch{1.5} \begin{array}{c:c} Event\ X & Event\ Y \\ \hline (1,3) & (2,1) \\ (2,2) & (2,2) \\ (1,3) & (2,3) \\ & (2,4) \\ & (2,5) \\ & (2,6) \\ & (5,1) \\ & (5,2) \\ & (5,3) \\ & (5,4) \\ & (5,5) \\ & (5,6) \\ \end{array}$$