Question

For the given situation,


find the probability of getting an even number when an unbiased die is rolled.

Also, find the desirable outcome in this case.

• A. $P\left(E\right)=\frac{1}{2}$
  Desired outcome $=$ Getting an odd number
• B. $P\left(E\right)=\frac{1}{2}$
  Desired outcome $=$ Getting an even number

Answer 1

The correct option is A $P\left(E\right)=\frac{1}{2}$

Desired outcome $=$ Getting an odd number
When we roll a die, the sample space $S$ obtained is:
$S=\{1,2,3,4,5,6\}$

We are given with $2$ cases:

$\underset{–}{Case1:}$

Getting an odd number when a die is rolled. The sample space $S_1$ for this case:
$S_1=\{1,3,5\}$


$\underset{–}{Case2:}$

Getting an even number when a die is rolled. The sample space $S_2$ for this case:
$S_2=\{2,4,6\}$


Let $P\left(E\right)$ denotes the probability of getting an even number when a die is rolled.
$P\left(E\right)=\frac{Numberoffavorableoutcomes}{Totalnumberofoutcomes}$

In this case,
Number of favorable outcomes $=3$, i.e., $\{2,4,6\}$
Total number of outcomes $=6$, i.e., $\{1,2,3,4,5,6\}$

$P\left(E\right)=\frac{3}{6}$

$P\left(E\right)=\frac{1}{2}$

The probability of getting an even number when an unbiased die is rolled is $\frac{1}{2}$.


The desirable outcome would be "getting an odd number" as this case signifies the "WIN" situation.

Therefore, option (b.) is the correct answer.