Question

For the given situation,


find the probability of getting an odd number when a die is rolled.

Also, check whether desired outcome is same as favorable outcome.

• A. $\text{P(O)}=\frac{1}{2}$
  
  The desired outcome is same as favorable outcome, i.e., Getting an odd number.
• B. $\text{P(O)}=\frac{1}{2}$
  
  The desired outcome is not the same as favorable outcome, i.e., Getting an odd number.
• C. $\text{P(O)}=\frac{1}{2}$
  
  The desired outcome is same as favorable outcome, i.e., Getting an even number.
• D. $\text{P(O)}=\frac{1}{2}$
  
  The desired outcome is not the same as favorable outcome, i.e., Getting an even number.

Answer 1

The correct option is A $\text{P(O)}=\frac{1}{2}$


The desired outcome is same as favorable outcome, i.e., Getting an odd number.
Let $S$ be the sample space obtained when we roll a die.
$S=\{1,2,3,4,5,6\}$

Let $\text{P(O)}$ denotes the probability of getting an odd number when a die is rolled.

$\text{P(O)}=\frac{\text{Number of favorable outcome}}{\text{Total number of outcomes}}$

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

$\text{P(O)}=\frac{3}{6}$

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

The probability of obtaining an odd number when a die is rolled is $\frac{1}{2}$.
Favorable outcome $=$ Getting an odd number

The desired outcome is "getting an odd number" as getting an odd number signifies a "WIN" situation.


The desired outcome is same as favorable outcome, i.e., Getting an odd number.

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