Two dice are rolled once. Find the probability of getting such numbers on the two dice,
(b) Sum of numbers on the two dice is atmost 5.

Answer

To find the probability of getting a sum of numbers on two rolled dice that is at most 5, we can follow these steps:

### Step 1: Determine the Total Outcomes
When two dice are rolled, each die has 6 faces. Therefore, the total number of outcomes when rolling two dice is:
\[ \text{Total Outcomes} = 6 \times 6 = 36 \]

### Step 2: Identify Favorable Outcomes
Next, we need to find the combinations of numbers on the two dice that result in a sum of at most 5. We can list these combinations:

- For a sum of 2: (1, 1)
- For a sum of 3: (1, 2), (2, 1)
- For a sum of 4: (1, 3), (2, 2), (3, 1)
- For a sum of 5: (1, 4), (2, 3), (3, 2), (4, 1)

Now, let's count the favorable outcomes:
- Sum of 2: 1 outcome
- Sum of 3: 2 outcomes
- Sum of 4: 3 outcomes
- Sum of 5: 4 outcomes

Adding these together:
\[ 1 + 2 + 3 + 4 = 10 \text{ favorable outcomes} \]

### Step 3: Calculate the Probability
The probability \( P \) of an event is given by the formula:
\[ P = \frac{\text{Number of Favorable Outcomes}}{\text{Total Outcomes}} \]
Substituting the values we have:
\[ P = \frac{10}{36} \]

### Step 4: Simplify the Probability
We can simplify \( \frac{10}{36} \) by dividing both the numerator and the denominator by their greatest common divisor, which is 2:
\[ P = \frac{10 \div 2}{36 \div 2} = \frac{5}{18} \]

### Final Answer
The probability of getting a sum of numbers on the two dice that is at most 5 is:
\[ \frac{5}{18} \]

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