Question

A die is rolled, and events are defined as
$A:$ outcome is $7$
$B:$ outcome is less than $9$

Which of the following statement(s) is(are) true for above events?

• A. $A$ is an impossible event
• B. $A$ is a certain event
• C. $B$ is a certain event
• D. $B$ is an impossible event

Answer 1

Answer: (A), (C)

$B$ is a certain event

When a die is rolled, all the possible outcomes $=\{1,2,3,4,5,6\}$

As we can see, $7$ does not belong the the set of the possible outcomes. So, on rolling a die $7$ will never appear. Hence, $A$ is an impossible event.

Again, we can see, all the possible outcomes is less than $9,$ we will always get the outome as less than $9$ upon rolling a die. Hence, $B$ is a certain event.