# Why is the last answer correct?

In the first lesson of this mission it says:
“P(A ∪ B) means finding the probability that A occurs or B occurs (this doesn’t exclude the situation where both A and B occur)”

But the answer to P(GL ∪ RAM) is:

``````p_gl_or_ram = p_gl + p_ram - p_gl_and_ram
``````

But this does exclude the situation where A and B both occur…
I thought the answer would be:

``````p_gl_or_ram = p_gl + p_ram
``````
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Hi @mephianna:

Generally this is correct when A and B are mutually exclusive (i.e. they do not intersect), so `p_gl_and_ram` is zero in this case.

The general formula to remember is still `P(A ∪ B) = P(A) + P(B) − P(A ∩ B)`

Hope this clarifies!

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Thank you for you response!

I think you explanation is right.

The explanation in the text is confusing, and I think that at this point in the course we have not seen the formula `P(A ∪ B) = P(A) + P(B) − P(A ∩ B)` yet.

But with you help and the explanation here https://www.statisticshowto.com/probability-and-statistics/probability-main-index/probability-of-a-and-b/ it was able to explain it to myself like this:

Draw one card, with two not mutually exclusive events: what is the chance of drawing a Jack or a Heart?

``````p(Jack) = 4/52

p(Heart) = 13/52

p(Jack of Hearts) = 1/52

p(Jack or Heart) = p(Jack) + p(Heart) – p(Jack of Hearts) = 4/52 + 13/52 – 1/52 = 16/52
``````

Or draw one card, with two mutually exclusive events, what is the chance of drawing a Jack or a Queen?

``````p(Jack) = 4/52

p(Queen) = 4/52

p(Jack and Queen) = 0

p(Jack or Queen) = p(Jack) + p(Heart) – p(Jack and Queen) = 4/52 + 4/52 – 0 = 8/52
``````

In the case of mutually exclusive events the `− P(A ∩ B)` part or `-0` can be left out since the result is the same…

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Yup that is correct @mephianna

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