Question

2 six sided dice are rolled. the rolls re independent. what is the probability that at least one die rolls a 5?

Answer 1

are*

Answer 2

the only way i can do this question is by drawing out a table, but id like to be able to understand a formula

Answer 3

answer is 11/36

Answer 4

The outcomes are marked, as you have probably done.
The number eleven / 36 is obtained by adding
1. probability of having once die rolling a 5 (1/6)
2. probability of the other die rolling a 5 (1/6)
LESS
3. probability of both dice rolling a 5 (A and B) = 1/6*1/6=1/36
We need to subtract P(A&B) because we have counted it twice in items 1 & 2.
You can see this from the diagram:
horizontal and vertical rows intersect. That's the one that is counted twice.

In general, it is:
P(A OR B) = P(A)+P(B)-P(A AND B)