Question

If a fair die is rolled, and sample space is defined as, sample space $=\left\{\text{Even number, Odd number}\right\},$ then the outcomes are equally likely.

• A. True
• B. False

Answer 1

The correct option is A True

$\underset{–}{\text{Equally Likely Outcomes}:}$
The outcomes in a sample space are $\text{equally likely}$ if each outcome has the $\text{same probability}$ of occurring.

A die is rolled and sample space is defined as, sample space $=\left\{\text{Even number, Odd number}\right\}$

In above given sample space, there are two outcomes 'Even number' and 'Odd number'.

Now, as we know, if a fair die is rolled,

$\text{P(Odd number)}=\frac{1}{2}$

$\text{P(Even number)}=\frac{1}{2}$

Here, the probability of both the outcomes are equal, hence, these are equally likely outcomes.

Therefore, the given statement is true.