Question

Match the occurrence of the given events with their probabilities, with respect to rolling a single dice.

• A. $\frac{1}{2}$
• B. $\frac{1}{3}$
• C. $\frac{2}{3}$

Answer 1

The sample space for a single die roll is {1,2,3,4,5,6}
The number of possible events = 6

Let's look at the events.

1) Occurrence of an even number:
Favourable outcomes = {2,4,6}
Number of favourable outcomes = 3
Probability = $\frac{3}{6}=\frac{1}{2}$


2) Occurrence of a multiple of 3:
Favourable outcomes = {3,6}
Number of favourable outcomes = 2
Probability = $\frac{2}{6}=\frac{1}{3}$

3) Occurrence of a number ≤ 4:
Favourable outcomes = {1,2,3,4}
Number of favourable outcomes = 4
Probability = $\frac{4}{6}=\frac{2}{3}$