Question

If two dice are thrown together then find the probability of getting the sum eight.

Hint:

For problems involving two dice, it can be helpful to visualize or quickly sketch a 6x6 grid of all possible sums. This helps ensure you don't miss any favorable outcomes, especially for more complex conditions.

Answer 1

Step 1: Understanding the Concept:
This is a problem of classical probability. The probability of an event is the ratio of the number of outcomes favorable to the event to the total number of possible outcomes in the sample space.
Step 2: Key Formula or Approach:
\[ \text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \] Step 3: Detailed Explanation:
When two fair six-sided dice are thrown, each die has 6 possible outcomes. The total number of possible outcomes in the sample space is: \[ \text{Total outcomes} = 6 \times 6 = 36 \] We want to find the probability of getting a sum of eight. Let's list all the pairs of outcomes (die 1, die 2) that sum to 8: \[ (2, 6) \] \[ (3, 5) \] \[ (4, 4) \] \[ (5, 3) \] \[ (6, 2) \] There are 5 such pairs. So, the number of favorable outcomes is 5.
Now, we can calculate the probability: \[ P(\text{sum is 8}) = \frac{5}{36} \] Step 4: Final Answer:
The probability of getting the sum eight is \( \frac{5}{36} \).