A die is thrown twice. Each time the number appearing on it is recorded. Describe the following events:

(i) A = Both numbers are odd.


(ii) B = Both numbers are even


(iii) C = sum of the numbers is less than 6.


Also, find A ∪ B, A ∩ B, A ∪ C, A ∩ C. Which pairs of events are mutually exclusive.

Given: A dice is thrown twice. And each time number appearing on it is recorded.


To Find: Describe the given events.


Explanation: when the dice is thrown twice then the number of sample spaces are 62 = 36


Now,


The possibility both odd numbers are:


A = {(1, 1), (1, 3), (1, 5), (3, 1), (3, 3), (3, 5), (5, 1), (5, 3), (5, 5)}


Since, Possibility of both even numbers are:


B = {(2, 2)(2, 4)(2, 6)(4, 2)(4, 4)(4, 6)(6, 2)(6, 4)(6, 6)}


And, Possible outcome of sum of the numbers is less than 6


C = {(1, 1)(1, 2)(1, 3)(1, 4)(2, 1)(2, 2)(2, 3)(3, 1)(3, 2)(4, 1)}


Therefore,


(AՍB) = {(1, 1), (1, 3), (1, 5), (3, 1), (3, 3), (3, 5), (5, 1), (5, 3), (5, 5) (2, 2)(2, 4)(2, 6)(4, 2)(4, 4)(4, 6)(6, 2)(6, 4)(6, 6)}


(AՌB) = {Փ}


(AUC) = {(1, 1), (1, 3), (1, 5), (3, 1), (3, 3), (3, 5), (5, 1), (5, 3), (5, 5) (1, 2)(1, 4)(2, 1)(2, 2)(2, 3)(3, 1)(3, 2)(4, 1)}


(AՌC) = {(1, 1)(1, 3)(3, 1)}


Hence, (AՌB) = Փ and (AՌC)≠Փ, A and B are mutually exclusive, but A and C are not.


6