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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"
"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)
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