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To solve this problem, let's break down the information provided:

- We are rolling a 6-sided die.
- Event \( B \) is defined as the die showing a number greater than 2.
- We need to find \( P(B^c) \), which is the probability that \( B \) does *not* occur.

### Step 1: Define Event \( B \)
Since \( B \) is the event that the die shows a number greater than 2, the possible outcomes for \( B \) are \( \{3, 4, 5, 6\} \). This gives us 4 favorable outcomes for \( B \).

### Step 2: Find \( B^c \)
The complement event \( B^c \) represents the event where the die shows a number *not* greater than 2. The outcomes for \( B^c \) would be \( \{1, 2\} \), giving us 2 favorable outcomes for \( B^c \).

### Step 3: Calculate \( P(B^c) \)
Since there are 6 possible outcomes when rolling a die, the probability of \( B^c \) is:
\[
P(B^c) = \frac{\text{Number of favorable outcomes for } B^c}{\text{Total number of outcomes}} = \frac{2}{6} = 0.333
\]

### Answer
The probability \( P(B^c) \) is \( 0.333 \) when rounded to three decimal places.

Would you like a more detailed breakdown of any part of this solution? 

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Here are five related questions that might deepen your understanding:

1. What is the probability of rolling an even number on a 6-sided die?
2. How would you calculate \( P(A \cup B) \) for events \( A \) and \( B \)?
3. What is the probability of rolling a number greater than 4 on a 6-sided die?
4. How would the probability change if the die had 8 sides instead of 6?
5. What is the probability of rolling a number less than 5 on a 6-sided die?

**Tip:** When calculating probabilities, always check if the event or its complement might be easier to evaluate. This can simplify complex calculations.

Suppose that you roll a 6-sided die. Let A be the event that the die shows an even number, and let B be the event that the die shows a number that is greater than 2. Find P(B^c). Enter your answer as a decimal probability rounded to three decimal places.

Calculate the probability that a 6-sided die does not show a number greater than 2. This problem covers probability concepts, including complementary events and basic probability rules, and is suitable for students in Grades 7-9.

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