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
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!
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…
Yup that is correct @mephianna