Probability Question (1 Viewer)

[frenzal_dude]

Hi, just need a bit of help with this question:

P(A or B) = 15/16, P(A and B) = 2/16, P(A) = 6/16, P(B) = ?

I know the answer is P(B) = 11/16,
but I've got no idea how to get that answer.
I know or means + and 'and' means * but I still got the wrong answer.

 

[shinn]

Using the inclusion - exclusion principle, we have:
P(A or B) = P (A) + P (B) - P(A and B)
Substituting, 15/16 = 6/16 + P(B) - 2/16
So P(B) = 11/16.

Alternatively, you can draw a Ven-diagram with two circles sharing an intersection.
Labeling the first circle A and other circle B. You can assume there is a total of 16 items because all the denominators are 16. Then you just need to put the correct amount of items in each region and so you can find the total no. of items in B. This over 16 will be P(B).

 

[frenzal_dude]

thankyou!