To solve this problem, let's analyze the information provided.

Step 1: Determine the number of elements in the sample space $n(S)$

Since two 6-sided dice are rolled, each die has 6 possible outcomes. Therefore, the total number of outcomes when rolling two dice is: $n(S) = 6 \times 6 = 36$

Step 2: Determine the number of elements in event $E$

Event $E$ represents rolling doubles (both dice showing the same number of pips). The possible doubles are:

• (1,1)
• (2,2)
• (3,3)
• (4,4)
• (5,5)
• (6,6)

There are 6 doubles, so: $n(E) = 6$

Step 3: Find the probability of event $E$

The probability of an event $E$ is given by: $P(E) = \frac{n(E)}{n(S)}$ Substituting the values: $P(E) = \frac{6}{36} = \frac{1}{6}$

Summary of Answers

• $n(S) = 36$
• $n(E) = 6$
• Probability of event $E$: $\frac{1}{6}$

Would you like further clarification on any of these steps?

Additional Related Questions

1. What is the probability of rolling a sum of 7 with two dice?
2. How many outcomes are there if three 6-sided dice are rolled instead?
3. What is the probability of rolling two different numbers?
4. How does the probability of rolling doubles change if a 10-sided die is used instead?
5. What is the probability of getting a sum of 5 when rolling two dice?

Tip:

When dealing with probabilities, always ensure the sample space accounts for all possible outcomes to avoid errors in calculating probabilities.