Probability

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) = .
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) = . 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) = . The statement says the probability is , 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) = . 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) = . 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.