Hey guys, i notoo great at maths and am stuck on this question..
Given that for two events A and B, Pr(A) = .6, Pr(B) = 0.3 and Pr(B|A) = 0.1, find;
Pr(AnB) (the n is the upside down loop)
Pr(A|B)
Can anyone explain this please?
Hey guys, i notoo great at maths and am stuck on this question..
Given that for two events A and B, Pr(A) = .6, Pr(B) = 0.3 and Pr(B|A) = 0.1, find;
Pr(AnB) (the n is the upside down loop)
Pr(A|B)
Can anyone explain this please?
Pr(A n B) is the probability of both A and B happening (the n is an intersection sign). Pr(A|B) is the probability that A happens given that B happens: so P(A|B) = Pr(A n B) / Pr(B).
In your problem you're given Pr(B|A) which is Pr(B n A) / Pr(A). But Pr(A n B) = Pr(B n A): the event A and B happen is the same as the event B and A happen. You now have all the data required to find Pr(A n B) and Pr(A|B).
Incidentally Pr(A|B) and Pr(B|A) are quite different things. Think up a real-life example!
You've said that Pr(A n B) is 0.9. Where did that come from? Did you get it just by adding Pr(A) to Pr(B)? If so, that isn't valid. (Did you by any chance see the word 'and' and assume that meant you had to add things? It doesn't always ...) You can't necessarily tell the probability of two events happening together from the probability of each of them individually (try to think of some examples).
We have Pr(B|A) = Pr(B n A) / Pr(A). You're told Pr(B|A) = 0.1 and Pr(B) = 0.6. That tells you that Pr(B n A) = Pr(B|A) Pr(A) = X (work this out for yourself!). But A n B is the same as B n A: they both mean that each of A and B happens. Now Pr(A|B) = Pr(A n B)/Pr(B) = X / 0.3 = Y (again, work this out for yourself!). Compare Y with your teacher's answer.
BTW don't feel too bad if you don't get this immediately. A medical professor is currently appearing before a tribunal here in the UK accused of misconduct for having given 'expert' testimony in a previous criminal trial in which he allegedly confused Pr(A|B) with Pr(B|A).
Try this:
Given:
1. Pr(A) = 0.6
2. Pr(B) = 0.3
3. Pr(B|A) = 0.1
Wanted:
Pr(AnB)
Pr(A|B)
Definition:
4. Pr(A|B) = Pr(AnB)/Pr(B)
5. Pr(B|A) = Pr(BnA)/Pr(A)
Working:
6. Pr(BnA) = Pr(A) Pr(B|A) ... rearranging (5)
7. Pr(BnA) = 0.06 ... substituting (1) and (3) in (6)
8. Pr(AnB) = Pr(BnA) ... because AnB and BnA are the same event,
namely, both A and B happen
9. Pr(AnB) = 0.06 ... substituting (7) in (8)
10. Pr(A|B) = 0.2 substituting (1) and (9) in (4)