3) .
4) .
Can you finish?
Hi all, I`ve got an exam coming up in just over a week which will contain a question like this one.
From the attached Venn diagram work out
1) Determine P(A) and P(B)
2) Determine P(B|A) and P(A|B)
3) Determine P(¬B|A) and compare it with P(B|A)
4) Determine P(B|¬A)
5) Determine P(¬B|¬A) and compare it with P(B|¬A)
6) Determine P(¬A|¬B)
I don`t understand from question 3 onwards, can anybody please help me?
cheers.................
3) P(¬B|A) is the probability that B will occur given that A has occured. You know P(A). Now you just need the probability that B won't occur and A will, which is 13/Total. So you just do P(¬B and A)/P(A) = 13/824. Notice, this is 1-P(B|A)
4) This is the probability that B will occur given that A hasn't occured. You know P(¬A)=1-P(A). So, you just need P(B and ¬A), which is 124/Total. So it's just P(B and ¬A)/P(¬A). Notice that this will be [P(B)-P(B|A)P(A)]/P(¬A) by the law of total probability
You should get the idea now.