Question

If a fair die is rolled and sample space is defined as, sample space $=\{1,2,3,4,5,6\}$, 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 $=\{1,2,3,4,5,6\}$

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

$\text{P(1) = P(2) = P(3) = P(4) = P(5)}$

$=\text{P(6)}=\frac{1}{6}$

Here, the probability of each outcome is equal. Therefore, the outcomes of the given sample space are equally likely.

Hence, the given statement is true.