Question

A die is thrown once. The probability of getting a prime number will be

• A. 1
• B. \( \frac{1}{2} \)
• C. \( \frac{2}{3} \)
• D. \( \frac{1}{3} \)

Hint:

Be careful with the definition of a prime number. Remember that 1 is not a prime number. This is a common point of confusion that can lead to an incorrect answer. The smallest prime number is 2.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
Probability is the measure of the likelihood of an event occurring. It is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.
Step 2: Key Formula or Approach:
\[ \text{Probability of an event} = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}} \] Step 3: Detailed Explanation:
When a standard six-sided die is thrown once, the set of all possible outcomes (the sample space) is:
\[ S = \{1, 2, 3, 4, 5, 6\} \] The total number of possible outcomes is 6.
The event we are interested in is "getting a prime number". A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself.
The prime numbers in the sample space S are:
\[ \{2, 3, 5\} \] The number of favorable outcomes is 3.
Now, calculate the probability:
\[ P(\text{prime number}) = \frac{3}{6} = \frac{1}{2} \] Step 4: Final Answer:
The probability of getting a prime number is \( \frac{1}{2} \).