Question

A fair die is rolled once, which of the following statement(s) is(are) true?

• A. Outcome of an even number is an even chance event.
• B. Outcome of an even number is an unlikely event.
• C. Outcome of a number greater than two is a likely event.
• D. Outcome of a number greater than two is an unlikely event.

Answer 1

Answer: (A), (C)

Outcome of a number greater than two is a likely event.

Let's list the probabilities of different types of events:
$\underset{–}{\text{Given}:}$
A fair die is rolled once
$\therefore SampleSpace=\{1,2,3,4,5,6\}$
$\Rightarrow$ Total number of possible outcomes $=6$

Now, let's find the probability of each of the given options one-by-one:

As in first option, outcome is an even number,
Favorable outcomes $=\{2,4,6\}$
$\therefore$ Number of favorable outcomes $=3$

$\text{Probaility(Even)}=\frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}$

$\text{Probaility(Even)}=\frac{3}{6}$

$\text{Probaility(Even)}=\frac{3}{3\times 2}$

$\text{Probaility(Even)}=\frac{1}{2}=0.5$

As we can see, $\text{Probaility(Even)}=0.5,$ outcome of an even number for the given experiment is a $\text{even chance event}.$
$\underset{–}{}$

In third option, outcome is greater than two,
$\therefore$ Favorable outcome $=\{3,4,5,6\}$
$\Rightarrow$ Number of favorable outcome $=4$

$\text{Probability{>2}}=\frac{\text{Number of favorable outcome}}{\text{Total number of possible outcomes}}$

$\text{Probability{>2}}=\frac{4}{6}$

$\text{Probability{>2}}=\frac{2\times 2}{3\times 2}=\frac{2}{3}$

$\Rightarrow 0.5<\frac{2}{3}<1$

$\Rightarrow 0.5<\text{Probability{>2}}<1$

As we can see, $\Rightarrow 0.5<\text{Probability{>2}}<1,$ outcome of a number greater than two for the given experiment is a $\text{likely event}.$