SOLUTION: Given that P(A or B) = 1/3, P(A) = 1/6, and P(A and B) = 1/8, find P(B). 7/24 is the answer but I would really love to know why. This question is worded in a very confusing manner

Question 276406: Given that P(A or B) = 1/3, P(A) = 1/6, and P(A and B) = 1/8, find P(B).
7/24 is the answer but I would really love to know why. This question is worded in a very confusing manner.
Found 2 solutions by stanbon, edjones:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Given that P(A or B) = 1/3, P(A) = 1/6, and P(A and B) = 1/8, find P(B).
7/24 is the answer but I would really love to know why
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General Formula:
P(A or B) = P(A) + p(B) - P(A and B)
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Substitute:
1/3 = (1/6) + P(B) - 1/8
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Multiply thru by 24 to get:
8 = 4 + 24P(B) - 3
24P(B) = 7
P(B) = 7/24
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Cheers,
Stan H.
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Answer by edjones(8007) (Show Source): You can put this solution on YOUR website!
Become familiar with Venn diagrams and this will become much simpler.
In the intersection of the 2 circles put 1/8.
1/6 - 1/8 = 1/24 put this in the semicircle to left of 1/8
1/3 is the union of the 2 circles.
1/24 + 1/8 + x = 1/3
x=1/6 put this in the semicircle right of 1/8
1/8 + 1/6 = 7/24 P(B)
.
Ed
.

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