Question

two dice are rolled. find the probability of the following event. the first die is 6 or the sum is 6. the probability of the event \the first die is 6 or the sum is 6\ is (type an integer or a simplified fraction.)

Explanation:

Step1: Calculate total number of outcomes

When two dice are rolled, each die has 6 possible outcomes. So the total number of outcomes is $6\times6 = 36$.

Step2: Calculate number of outcomes where first die is 6

If the first die is 6, the second die can be 1, 2, 3, 4, 5, 6. So there are 6 outcomes: (6,1), (6,2), (6,3), (6,4), (6,5), (6,6).

Step3: Calculate number of outcomes where sum is 6

The possible pairs are (1,5), (2,4), (3,3), (4,2), (5,1), which is 5 outcomes.

Step4: Calculate number of overlapping outcomes

The overlapping outcome (where first die is 6 and sum is 6) is none.

Step5: Use the addition - rule of probability

The number of favorable outcomes for the event "first die is 6 or sum is 6" is $6 + 5=11$.
The probability $P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}=\frac{11}{36}$.

Answer:

$\frac{11}{36}$