Question

If two dice are thrown together, then find the probability of getting at least one 6.

Hint:

To calculate the probability of at least one event occurring, use the complementary approach: \( P(\text{at least one event}) = 1 - P(\text{no event}) \).

Answer 1

Step 1: Total Number of Outcomes.
When two dice are thrown, the total number of possible outcomes is: \[ 6 \times 6 = 36 \] This is because each die has 6 faces, and both dice are independent.
Step 2: Favorable Outcomes.
The favorable outcomes are those where at least one die shows a 6. We can calculate this using the complementary approach, i.e., the probability of getting at least one 6 is equal to 1 minus the probability of getting no 6 on either die. - The probability of not getting a 6 on one die is \( \frac{5}{6} \). - The probability of not getting a 6 on either die (both dice showing numbers other than 6) is: \[ \frac{5}{6} \times \frac{5}{6} = \frac{25}{36}. \] Therefore, the probability of getting at least one 6 is: \[ 1 - \frac{25}{36} = \frac{36}{36} - \frac{25}{36} = \frac{11}{36}. \]
Step 3: Conclusion.
Thus, the probability of getting at least one 6 when two dice are thrown is: \[ P(\text{at least one 6}) = \frac{11}{36}. \]