A pair of dice is thrown . Find the probability of getting a sum of 10 or more , if 5 appears on the first die .

Answer

To solve the problem of finding the probability of getting a sum of 10 or more when a pair of dice is thrown and the first die shows a 5, we can follow these steps:

### Step 1: Understand the Problem
We are given that the first die (let's call it Die 1) shows a 5. We need to find the possible outcomes for the second die (Die 2) such that the total sum of both dice is 10 or more.

**Hint:** Focus on the fixed value of the first die and how it affects the second die.

### Step 2: Determine the Required Sum
Since Die 1 shows a 5, we need to find the values of Die 2 that will give us a total of 10 or more. This means we need:
\[ 5 + \text{Die 2} \geq 10 \]
This simplifies to:
\[ \text{Die 2} \geq 5 \]

**Hint:** Rearranging the equation will help you find the minimum value for Die 2.

### Step 3: Identify Possible Values for Die 2
The possible values for Die 2 (since it is a die) are 1, 2, 3, 4, 5, and 6. From our requirement, Die 2 must be at least 5. Therefore, the possible values for Die 2 are:
- 5
- 6

**Hint:** List out the values of Die 2 that meet the condition.

### Step 4: Count Favorable Outcomes
The favorable outcomes that satisfy the condition of having a sum of 10 or more are:
1. (5, 5) → Sum = 10
2. (5, 6) → Sum = 11

Thus, there are **2 favorable outcomes**.

**Hint:** Make sure to count all combinations that meet the criteria.

### Step 5: Calculate Total Outcomes
Since we are only concerned with the outcomes of Die 2 (given that Die 1 is fixed at 5), there are a total of 6 possible outcomes for Die 2 (1 through 6).

**Hint:** Remember that the total outcomes are based on the number of possibilities for the second die.

### Step 6: Calculate Probability
The probability \( P \) of an event is given by the formula:
\[ P = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \]
Substituting the values we have:
\[ P = \frac{2}{6} = \frac{1}{3} \]

**Hint:** Simplifying the fraction will give you the final probability.

### Final Answer
The probability of getting a sum of 10 or more when the first die shows a 5 is:
\[ \frac{1}{3} \]