Question

Let sample space, S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. Let us define the following events
A: "set of numbers divisible by 2".
B: "set of numbers divisible by 3".
Then what should be the event C such that events A, B and C are mutually exhaustive?

• A. {1, 6, 9}
• B. {1, 5, 7}
• C. {7, 0, 5}
• D. {4, 8, 9}

Answer 1

The correct option is B {1, 5, 7}

A = {2, 4, 6, 8, 10}
B = {3, 6, 9}
$\Rightarrow A\cup B=\{2,3,4,6,8,9,10\}$
Events A, B and C are mutually exhaustive when $A\cup B\cup C=S\mathrm{So},C=S-\left(A\cup B\right)\mathrm{Therefore},C=\{1,5,7\}$