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: Conceptual Foundation: This exercise focuses on calculating elementary probabilities associated with a single roll of a standard six-sided die. The set of all possible outcomes, known as the sample space, is S = {1, 2, 3, 4, 5, 6}. The total count of these outcomes is 6. The probability of any given event E is determined by the formula: P(E) = (Number of favorable outcomes) / (Total number of outcomes).
Step 2: Methodology: We will assess the probability for each of the given statements (A), (B), (C), and (D) to ascertain their validity.
Step 3: Detailed Analysis: (A) Probability of rolling a number greater than 4: The outcomes exceeding 4 are {5, 6}. This yields 2 favorable outcomes. P(A) = \( \frac{2}{6} = \frac{1}{3} \). This statement is correct.
(B) Probability of rolling a number greater than or equal to 4: The outcomes meeting or exceeding 4 are {4, 5, 6}. This provides 3 favorable outcomes. P(B) = \( \frac{3}{6} = \frac{1}{2} \). The assertion in the statement is \( \frac{1}{3} \), rendering this statement incorrect.
(C) Probability of rolling a number less than or equal to 3: The outcomes not exceeding 3 are {1, 2, 3}. This results in 3 favorable outcomes. P(C) = \( \frac{3}{6} = \frac{1}{2} \). This statement is correct.
(D) Probability of rolling a number less than or equal to 6: The outcomes not exceeding 6 are {1, 2, 3, 4, 5, 6}. This comprises 6 favorable outcomes. P(D) = \( \frac{6}{6} = 1 \). This represents a certain event. This statement is correct.
The statements identified as correct are (A), (C), and (D).
Step 4: Conclusion: The correct option corresponds to the selection encompassing (A), (C), and (D) exclusively.