Hiren G.

asked • 12/01/16

P(a) = 0.5 , p(b) = 0.7 what is p(a | b)

I am trying to learn conditional probality but not able to figure solution for this any solution would be of great help

2 Answers By Expert Tutors

By:

David S. answered • 12/01/16

Tutor
New to Wyzant

History (SAT and AP; European, World, U.S.), Multiple Subjects

See tutors like this
See tutors like this
Actually, this is quite solvable...since P(A) and P(B) = .5 x .7 = .35 and P(A|B) = .35/.7 = .5
Since P(A) = .5 and P(A|B) is also = .5, then we say that A is Independent from B.  There's no association between the variables, and therefore, knowing A doesn't give us any clue as to knowing B.
Upvote • 0 Downvote
More
Report

Kenneth S.

David, please consider a Venn diagram in which circles A & B partially overlap, with the three regions A only, A∩B and B only constituting the components of the A∪B figure-eight. The different regions are given their probability numbers in the following two examples(case studies).
 
Case I: if we place decimal values as follows, A-only could be 0.2, B-only could be 0.4, and P(A∩B) would could be 0.3.
Case II: A-only is 0.1, B-only is 0.3, then P(A∩B) would could be 0.4.
 
In Case I, P(A|B) = 0.3/0.7 = 3/7
In Case II,  P(A|B) = 0.4/0.7= 4/7.
 
Is this a sufficient counterexample?
Report

12/01/16

Hiren G.

what if events are dependent ?
Report

12/01/16

David S.

That's not what the original question gave...
Report

12/01/16

David S.

Actually, we don't use the term dependent here. Either the variables are Independent or Not.  Also, Independence has NOTHING to do with being mutually exclusive (i.e., disjoint).  For example, if the events A and B are mutually exclusive (i.e., disjoint), you might still say the events are not Independent, it just depends on the circumstances.  For example, you flip a coin.  The events of heads and tails are mutually exclusive (disjoint), however, knowing you have Heads on a certain flip means you KNOW that you didn't get Tails, so the events are NOT Independent.  
Report

12/01/16

Kenneth S.

David, I consulted with the most brilliant Math PH.D that I know, at the college at which I formerly taught, before my retirement, and he replied as follows.

The initial error David S. is making is to say that probability of A and B =.5*.7
That is not true. Unless we are told that A and B are independent, in which case we would have the intersection be the product of the probability. This problem is not solvable as is. More information is needed. Either the probability of the intersection or a statement regarding independence is required.
 
So I believe that my answer is CORRECT and (unfortunately) yours is not. 
Report

12/01/16

David S.

we can agree to disagree, but the fact remains that the students did not provide enough information and I was speculating what may have been provided...this was a freebie for me to do, and frankly it feels that no good deed goes unpunished...
Report

12/04/16

Still looking for help? Get the right answer, fast.

Ask a question for free

Get a free answer to a quick problem.
Most questions answered within 4 hours.

OR

Find an Online Tutor Now

Choose an expert and meet online. No packages or subscriptions, pay only for the time you need.