The probability of not getting a sum of 7 in a single throw with a pair of dice, is

Options

A. `1/6`
B. `2/3`
C. `1/3`
D. `5/6`

Answer

To find the probability of not getting a sum of 7 when throwing a pair of dice, we can follow these steps:

### Step 1: Determine the total number of outcomes
When throwing two dice, 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: Identify the outcomes that result in a sum of 7
Next, we need to find the combinations of the two dice that give us a sum of 7. The pairs that yield a sum of 7 are:
- (1, 6)
- (2, 5)
- (3, 4)
- (4, 3)
- (5, 2)
- (6, 1)

Counting these, we find there are 6 outcomes that result in a sum of 7.

### Step 3: Calculate the number of outcomes that do not result in a sum of 7
To find the number of outcomes that do not yield a sum of 7, we subtract the number of outcomes that do yield a sum of 7 from the total number of outcomes:
\[ \text{Outcomes not yielding a sum of 7} = \text{Total Outcomes} - \text{Outcomes yielding a sum of 7} = 36 - 6 = 30 \]

### Step 4: Calculate the probability of not getting a sum of 7
The probability of an event is given by the ratio of the number of favorable outcomes to the total number of outcomes. Therefore, the probability of not getting a sum of 7 is:
\[ P(\text{not getting a sum of 7}) = \frac{\text{Outcomes not yielding a sum of 7}}{\text{Total Outcomes}} = \frac{30}{36} \]

### Step 5: Simplify the probability
Now, we simplify the fraction:
\[ P(\text{not getting a sum of 7}) = \frac{30}{36} = \frac{5}{6} \]

Thus, the probability of not getting a sum of 7 in a single throw with a pair of dice is:
\[ \frac{5}{6} \]