Question

Two dice are rolled. Let us define the following events
A: "sum of numbers on dice is greater than
or equal to 10".
B: "at least one number is 5".
Which of the following option(s) is/are correct?

• A. Event A is a simple event.
• B. Events A and B are not mutually exclusive events.
• C. Event B is a compound event.
• D. Events A and B are mutually exclusive events.

Answer 1

Answer: (B), (C)

The correct options are
B Events A and B are not mutually exclusive events.
C Event B is a compound event.

For given experiment,
$A=\left\{\right(6,4),(5,5),(5,6),(6,4),(6,5),(6,6\left)\right\}B=\left\{\right(1,5),(2,5),(3,5),(4,5),(5,5),(6,5\left)\right\}$

We can see that element
$(6,5)$ is present in both the events. Therefore, they are not mutually exclusive.

Event B is a compound event as it contains more than one element.

Event A is not simple as it contains more than one element.