probiablty of getting exaclty 2 mlpites of 3 

To calculate the probability of getting exactly 2 multiples of 3 in two rolls of a die, we can follow these steps:

### Step 1: Identify the Probability of Each Relevant Event

1. **Probability of Rolling a Multiple of 3:**
   - The multiples of 3 on a six-sided die are 3 and 6.
   - There are 2 favorable outcomes (3 and 6) out of 6 possible outcomes.
   \[
   P(\text{Multiple of 3}) = \frac{2}{6} = \frac{1}{3}
   \]

2. **Probability of Rolling Not a Multiple of 3:**
   - The numbers that are not multiples of 3 are 1, 2, 4, and 5.
   - There are 4 favorable outcomes (1, 2, 4, 5) out of 6 possible outcomes.
   \[
   P(\text{Not a Multiple of 3}) = \frac{4}{6} = \frac{2}{3}
   \]

### Step 2: Calculate the Probability of Getting Exactly 2 Multiples of 3

To get exactly 2 multiples of 3 in two rolls, both rolls must be multiples of 3. Since each roll is independent, we multiply the probabilities:

\[
P(\text{Both rolls are multiples of 3}) = P(\text{Multiple of 3 on Roll 1}) \times P(\text{Multiple of 3 on Roll 2})
\]
\[
P(\text{Both rolls are multiples of 3}) = \frac{1}{3} \times \frac{1}{3} = \frac{1}{9}
\]

### Final Answer:
The probability of getting exactly 2 multiples of 3 in two rolls of a die is \( \frac{1}{9} \).

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**Related Questions:**
1. What is the probability of getting at least one multiple of 3 in two rolls?
2. How would the probability change if there were three rolls instead of two?
3. What is the probability of getting no multiples of 3 in two rolls?
4. How do we calculate the probability of

Explore how to calculate the probability of getting exactly 2 multiples of 3 in two rolls of a die. Understand the concepts of probability, independent events, and the multiplication rule. Suitable for students in Grades 9-12.

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