Two dice are rolled simultaneously . Find the probability of
getting atleast one'5'.

Options

A. `3/5`
B. `1/5`
C. `(5)/(36)`
D. `(11)/(36)`

Answer

To find the probability of getting at least one '5' when two dice are rolled, we can follow these steps:

### Step 1: Determine the total number of outcomes when rolling two dice.
When one die is rolled, there are 6 possible outcomes (1 through 6). Since two dice are rolled simultaneously, the total number of outcomes is:
\[ 6 \times 6 = 36 \]
**Hint:** Remember that the total outcomes for two independent events (like rolling two dice) is the product of the outcomes for each event.

### Step 2: Identify the favorable outcomes for getting at least one '5'.
We can find the number of favorable outcomes by considering the different scenarios where at least one die shows a '5'. These scenarios include:
1. The first die shows '5' and the second die shows anything (1, 2, 3, 4, 5, 6).
2. The second die shows '5' and the first die shows anything (1, 2, 3, 4, 5, 6).

However, we need to be careful not to double-count the outcome where both dice show '5'.

- Outcomes where the first die is '5': (5,1), (5,2), (5,3), (5,4), (5,5), (5,6) → 6 outcomes.
- Outcomes where the second die is '5': (1,5), (2,5), (3,5), (4,5), (5,5), (6,5) → 6 outcomes.

Now, we have counted (5,5) twice, so we need to subtract 1 from the total:
\[ 6 + 6 - 1 = 11 \]
**Hint:** When counting outcomes, make sure to account for any overlaps to avoid double counting.

### Step 3: Calculate the probability.
The probability of an event is given by the formula:
\[ \text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \]
Substituting the values we found:
\[ \text{Probability} = \frac{11}{36} \]
**Hint:** Always remember to express probability as a fraction of favorable outcomes over total outcomes.

### Final Answer:
The probability of getting at least one '5' when rolling two dice is:
\[ \frac{11}{36} \]