How Do You Calculate Conditional Probability Using a Probability Tree?

[hasnain721]

conditional probability help please

Homework Statement

Hi there,
I am doing s1 for this jan and i am finding it very difficult to cope up. Especially for probability. I have a cgp buk but stil its not very gud at probability. Here is a question from my text buk which i cud not understand : -




Two events A and B are such that P(A) = 3/4 , P(B l A) = 1/5 and P(B' l A') = 4/7. By use of a probability tree or other wise find :


a) P(A and B)

b) P(B)

c) P(A l B)



In addition, can some 1 suggest a gud buk for probability please.

Homework Equations

P(B l A) = P(A intersection B) / P(A)

The Attempt at a Solution

I got 'a' right by multiplying 3/4 by 1/5


Plz reply
Thanks
Hasnain Mir Mohammed

 

[hasnain721]

i hav worked it out now...thanks.

 

[piercas]

I can understand that probability can be a challenging concept to grasp, especially for those who are new to it. It's great that you are seeking help and trying to understand it better.

To solve this problem, you can use the formula for conditional probability: P(B|A) = P(A and B)/P(A). In this case, you already know P(A) and P(B|A), so you can rearrange the formula to solve for P(A and B).

a) P(A and B) = P(B|A) * P(A) = (1/5) * (3/4) = 3/20

b) To find P(B), you can use the formula P(B) = 1 - P(B'), where B' represents the complement of B. In this case, P(B') = P(B'|A') * P(A') = (4/7) * (1/4) = 1/7. Therefore, P(B) = 1 - 1/7 = 6/7.

c) P(A|B) = P(A and B)/P(B) = (3/20)/(6/7) = 7/40

As for a good book on probability, I would recommend "Introduction to Probability" by Dimitri P. Bertsekas and John N. Tsitsiklis. It is a widely used textbook in many universities and provides a thorough and clear explanation of probability concepts. Additionally, you can also try practicing more problems and seeking help from your teacher or peers if you still have difficulty understanding certain concepts. Best of luck with your studies!