I am stumped...please help...I'm not sure what they are talking about with P (A and B) = 0

If P(A) = 2/3, P(B) = 1/6, and P(A and B) = 0, what can you say about P (A or B)?

Have you come across the formula

P(A or B) = P(A) + P(B) - P(A and B)
so we have
P(A or B) = 2/3 + 1/6 - 0 = 5/6

let me illustrate with an example:
Sam has 12 identical boxes in front of him. Inside 8 of the boxes are placed even numbers, inside 2 of them are placed odd numbers and inside the last two boxes are placed red marbles.

One box is picked at random.

Let A be: picking an even number.
Let B be: picking an odd number.

So P(A) = 8/12 = 2/3
P(B) = 2/12 = 1/6
P(picking an even AND an odd) = P(A and B) = 0 (NO WAY can that happen)

But picking an even OR an odd
= P(A or B) = 10/12 = 5/6
(there are 10 numbers in the boxes, either even or odd)

Now back to
P(A or B) = P(A) + P(B) - P(A and B)
= 2/3 + 1/6 = 5/6

Thank you, that really helped me!

To find the probability of the union of two events (A or B), you can use the formula:

P(A or B) = P(A) + P(B) - P(A and B)

In this case, we have:

P(A) = 2/3
P(B) = 1/6
P(A and B) = 0

Substituting these values into the formula, we get:

P(A or B) = (2/3) + (1/6) - 0 = 2/3 + 1/6 = 4/6 + 1/6 = 5/6

Therefore, the probability of event A or event B occurring (P(A or B)) is 5/6.

To understand why P(A and B) = 0 leads to the probability of events A or B occurring to be 5/6, we can consider the concept of mutually exclusive events. When two events are mutually exclusive, it means that they cannot occur at the same time. In this case, if P(A and B) = 0, it implies that events A and B do not have any outcomes in common. Hence, they are mutually exclusive.

When events A and B are mutually exclusive, the probability of their union (A or B) is simply the sum of their individual probabilities, which is P(A) + P(B). In other words, the events A and B cannot both occur simultaneously, so there is no need to subtract the probability of their intersection (P(A and B)) from the sum.

Therefore, when P(A and B) = 0, the formula for calculating P(A or B) simplifies to P(A) + P(B), and we obtain the probability of events A or B occurring.