Two dice are thrown at the same time. Find the probability of getting :
different numbers on both dice.

Answer

To solve the problem of finding the probability of getting different numbers on both dice when two dice are thrown, we can follow these steps:

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

### Step 2: Determine the number of favorable outcomes for different numbers
Next, we need to find the number of outcomes where the two dice show different numbers. To do this, we can first calculate the number of outcomes where both dice show the same number.

The pairs where both dice show the same number are:
- (1, 1)
- (2, 2)
- (3, 3)
- (4, 4)
- (5, 5)
- (6, 6)

This gives us a total of 6 outcomes where both dice show the same number.

### Step 3: Calculate the number of outcomes with different numbers
To find the number of outcomes where the two dice show different numbers, we subtract the number of same-number outcomes from the total outcomes:
\[ \text{Different outcomes} = \text{Total outcomes} - \text{Same outcomes} = 36 - 6 = 30 \]

### Step 4: Calculate the probability
The probability of getting different numbers on both dice is given by the ratio of the number of favorable outcomes to the total outcomes:
\[ \text{Probability} = \frac{\text{Favorable outcomes}}{\text{Total outcomes}} = \frac{30}{36} = \frac{5}{6} \]

### Final Answer
Thus, the probability of getting different numbers on both dice is:
\[ \frac{5}{6} \]

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