# Lesson: Applying the OR Rule

## Comment on Applying the OR Rule

### Hi,

Hi,
Is the mutually exclusive events and independent events means the same?
So if the events are independent then is P(event A and Event B)=0.

Plz can you clarify with this question:

"There is an 80% chance David will eat a healthy breakfast and a 25% chance that it will rain. If these events are independent, what is the probability that David will eat a healthy breakfast OR that it will rain"

### "Mutually Exclusive" does not

"Mutually Exclusive" does not mean the same as "Independent"

If events A and B are mutually exclusive, then P(A and B) = 0
If events A and B are independent, then P(A and B) = P(A) x P(B)

We want P(David eats a healthy breakfast OR it rains)

We know that P(A OR B) = P(A) + P(B) - P(A and B)

So, P(David eats a healthy breakfast OR it rains) = P(David eats healthy breakfast) + P(it rains) - P(eats healthy breakfast AND that it rains)
= 0.8 + 0.25 - (0.8 x 0.25)
= 0.8 + 0.25 - (0.2)
= 0.85

Does that help?

Cheers,
Brent

Thanks Brent