Question

If a fair die is rolled and sample space is defined as, sample space $=\{3,\text{not 3}\}$, then the outcomes are equally likely.

• A. True
• B. False

Answer 1

The correct option is B False

$\underset{–}{\text{Equally Likely Outcomes}:}$
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 $=\{3,\text{not 3}\}$

In above given sample space, there are two outcomes '$3$' and 'not $3$'.

Now, as we know, if a fair die is rolled,
P$\left(3\right)=\frac{1}{6}$ and
P$\left(\text{not 3}\right)=1-\text{P(3)}=1-\frac{1}{6}=\frac{5}{6}$

Here, probability of '$3$' and 'not $3$' are not equal, therefore, outcomes in the given sample space are not equally likely. Hence, the the given statement is false.