Question

Problem 5. Suppose two dice are tossed and the numbers on the upper faces are observed. Let S denote the set of all possible pairs that can be observed. The pairs can be listed, for example, by letting (2, 3) denote that a 2 was observed on the first die and a 3 on the second. Define the following subsets of S .A The number on the second die is odd. · B: The sum of the two numbers is odd. Describe the events An B and AU Bc in words and list all the outcomes in the events. (0.5 each)

Answer 1

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1. Ac and B = The number of second die is not odd and sum of 2 numbers is odd

= On 2nd die {2,4,6} and On the 1st die its odd number {1,3,5} [only if 1st die number is odd will the sum be odd]

So, Ac and B = Odd numbers on 1st die and Even numbers on 2nd die

2. A U Bc = 2nd die is odd {1,3,5} U Sum of two numbers is even (which means 2nd die should have odd ) - {1,3,5}

So, A U Bc = {1,3,5}

Answer 2

Suppose two dice are tossed and the numbers on the upper faces are observed. Let S denote

the set of all possible pairs that can be observed. [These pairs can be listed, for example, by

letting (2, 3) denote that a 2 was observed on the first die and a 3 on the second.]

a Define the following subsets of S:

A: The number on the second die is even.

B: The sum of the two numbers is even.

C: At least one number in the pair is odd.

b List the points in A,C, A ∩ B, A ∩ B, A ∪ B, and A ∩ C.