Question

An unbiased die is thrown and B is an event showing an odd number on top. Then $P(B)$ is:

• A. $\frac{1}{4}$
• B. $\frac{1}{3}$
• C. $\frac{1}{6}$
• D. $\frac{1}{2}$
• E. $\frac{1}{5}$

Hint:

Half the numbers on a standard die are odd, and half are even.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
We need to find the probability of an event occurring when an unbiased die is thrown. Probability is the ratio of the number of favorable outcomes to the total number of possible outcomes.
Step 2: Key Formula or Approach:
The formula for the probability of an event E is:
\[ P(E) = \frac{\text{Number of Favorable Outcomes}}{\text{Total Number of Possible Outcomes}} \] Step 3: Detailed Explanation:
The experiment is throwing a single unbiased die.
Total Number of Possible Outcomes:
When a standard die is thrown, the possible outcomes are the numbers on its faces: \{1, 2, 3, 4, 5, 6\}.
So, the total number of outcomes is 6.
Number of Favorable Outcomes:
The event B is "showing an odd number on top". The odd numbers in the set of possible outcomes are \{1, 3, 5\}.
So, the number of favorable outcomes for event B is 3.
Calculate the Probability P(B):
\[ P(B) = \frac{\text{Number of favorable outcomes for B}}{\text{Total number of possible outcomes}} = \frac{3}{6} \] Simplifying the fraction gives:
\[ P(B) = \frac{1}{2} \] Step 4: Final Answer:
The probability P(B) is \( \frac{1}{2} \).