A pair of dice is tossed once and X denotes the sum of numbers that appear on the two dice, then `P(X le 4)` =___________.

Answer

To solve the problem of finding \( P(X \leq 4) \) where \( X \) is the sum of the numbers appearing on two tossed dice, we can follow these steps:

### Step 1: Identify the Sample Space
When two dice are tossed, each die has 6 faces, so the total number of outcomes when tossing two dice is:
\[ 6 \times 6 = 36 \]
Thus, the sample space \( S \) consists of 36 possible outcomes.

### Step 2: Determine the Favorable Outcomes for \( X \leq 4 \)
We need to find all the combinations of the two dice that give a sum less than or equal to 4. The possible sums and their combinations are:

- **Sum = 2**:
- (1, 1)

- **Sum = 3**:
- (1, 2)
- (2, 1)

- **Sum = 4**:
- (1, 3)
- (2, 2)
- (3, 1)

Now, let's list all the favorable outcomes:
1. (1, 1) → Sum = 2
2. (1, 2) → Sum = 3
3. (2, 1) → Sum = 3
4. (1, 3) → Sum = 4
5. (2, 2) → Sum = 4
6. (3, 1) → Sum = 4

Counting these outcomes gives us a total of 6 favorable outcomes.

### Step 3: Calculate the Probability
The probability \( P(X \leq 4) \) is calculated as the ratio of the number of favorable outcomes to the total number of outcomes:
\[ P(X \leq 4) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{6}{36} = \frac{1}{6} \]

### Final Answer
Thus, the probability that the sum \( X \) is less than or equal to 4 is:
\[ P(X \leq 4) = \frac{1}{6} \]

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