Question

Suppose we throw a dice once. Then, which one of the following is/are correct?
(A) The probability of getting a number greater than 4 is \( \frac{1}{3} \).
(B) The probability of getting a number greater than or equal to 4 is \( \frac{1}{3} \).
(C) The probability of getting a number less than or equal to 3 is \( \frac{1}{2} \).
(D) The probability of getting a number less than or equal to 6 is 1.
Choose the correct answer from the options given below:

• A. (A), (B) and (D) only
• B. (B), (C) and (D) only
• C. (A), (C) and (D) only
• D. (A) and (D) only

Hint:

Pay close attention to the wording in probability problems, especially the difference between "greater than" and "greater than or equal to." This small difference changes the number of favorable outcomes and thus the probability.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
This problem involves calculating basic probabilities for a single roll of a standard six-sided die. The sample space (all possible outcomes) is S = \{1, 2, 3, 4, 5, 6\}. The total number of outcomes is 6.
Probability of an event E is given by P(E) = \( \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \).
Step 2: Key Formula or Approach:
We will evaluate the probability for each statement (A), (B), (C), and (D) and check if it is correct.
Step 3: Detailed Explanation:
(A) The probability of getting a number greater than 4:
The numbers greater than 4 are \{5, 6\}. There are 2 favorable outcomes.
P(A) = \( \frac{2}{6} = \frac{1}{3} \). This statement is correct.
(B) The probability of getting a number greater than or equal to 4:
The numbers greater than or equal to 4 are \{4, 5, 6\}. There are 3 favorable outcomes.
P(B) = \( \frac{3}{6} = \frac{1}{2} \). The statement says the probability is \( \frac{1}{3} \), so this statement is incorrect.
(C) The probability of getting a number less than or equal to 3:
The numbers less than or equal to 3 are \{1, 2, 3\}. There are 3 favorable outcomes.
P(C) = \( \frac{3}{6} = \frac{1}{2} \). This statement is correct.
(D) The probability of getting a number less than or equal to 6:
The numbers less than or equal to 6 are \{1, 2, 3, 4, 5, 6\}. There are 6 favorable outcomes.
P(D) = \( \frac{6}{6} = 1 \). This is a certain event. This statement is correct.
The correct statements are (A), (C), and (D).
Step 4: Final Answer:
The correct option is the one that includes (A), (C), and (D) only.