Question

A die is rolled and the outcomes are observed. Event A is an even number turns up and event B is a prime number turns up. Match the events on left with the outcomes on right.

$\begin{array}{cc}1.\text{Event A or B}& P.\{4,6\}\\ 2.\text{Event A and B}& Q.\left\{2\right\}\\ 3.\text{Event A but not B}& R.\{2,3,4,5,6,\}\\ 4.\text{Complementary event of B}& S.\{1,4,6\}\end{array}$

• A. 1 - R, 2 - Q, 3 - S, 4 - P
• B. 1 - Q, 2 - R, 3 - P, 4 - S
• C. 1 - R, 2 - Q, 3 - P, 4 - S
• D. 1 - R, 2 - S, 3 - Q, 4 - P

Answer 1

The correct option is C

1 - R, 2 - Q, 3 - P, 4 - S

Sample space associated with throwing a die s = {1, 2, 3, 4, 5, 6}
A: An even number turns up = {2, 4,6}
B: A prime number turns up
= {2, 3, 5}

1)Event A or B $\equiv A\cup B$
= {2, 3, 4, 5, 6}

2)Event A and B $\equiv A\cap B$
= {2}

3)Event A but not $B\equiv A-B$
= set of elements in A which are not in B
= {4, 6}

4)Complementary event of B = B^`

= {1, 4, 6}