Lesson: Applying the OR Rule

Comment on Applying the OR Rule

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"
greenlight-admin's picture

"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)

Now onto your question...

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

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