Conditional probability basic question

3 Brothers named A,B,C are calling a radiohost.The probability of A calling radio suscesfully is %48 ,B's %34 ,C's %18.And even if they reach the host , possiblity of host reading their messages; A-%14 ,B-%8,C%2.If we know host read messages of one of that brothers , what is the probability of the message reading is brother A's. $$P(A|B)=P(A \cap B)/P(B) = 0.48 * 0.14/ 0.22$$ Is that logic correct?

• Hi and welcome to math.SE! Please use LaTeX to format mathematics notation in your questions. – Jacob Errington Apr 24 '17 at 20:35
• I wish users would not downvote new users, just on the basis not using mathjax. (@JacobErrington mathjax $\neq$ LaTeX. They share a lot in common, but it is unreasonable to expect a new user to know how to format mathematics when they first post a question. The asker has clearly attempted to answer the question, and is asking whether the logic she/he used is correct. – amWhy Apr 24 '17 at 20:52
• @amWhy I do agree. – Iti Shree Apr 24 '17 at 21:02
• I'm sorry, @Jacob I did not mean to imply that you, yourself, downvoted the question because of its formatting. I just don't really like to see the first comment below a new asker's post harking on "formatting." It would have been great to have expressed your welcome, as you did. And at most suggest "in the future, it would help if you learned how to format your posts, as best as you can, as you're learning it..... – amWhy Apr 24 '17 at 21:11
• Thank you all of you guys for help :) – user3524633 Apr 24 '17 at 21:16

Probability of A calling the radiohost: $P(A)=48%$; $P(B)=34%$; $P(C)=18%$; Probability that host will read messages is $P\left(\frac{A}{H}\right)=14%$; $P\left(\frac{B}{H}\right)=8%$; $P\left(\frac{C}{H}\right)=2%$
Now you have to find probability that the message he reads is of A therefore the formula you must use is: $$P\left(\frac{H}{A}\right)= \frac{P\left(\frac{A}{H}\right) \cdot P(A)}{P \left(\frac{A}{H}\right)\cdot P(A)+P\left(\frac{B}{H}\right) \cdot P(B)+P\left(\frac{C}{H}\right) \cdot P(C)}$$
• Hey..Nice answer +1, I just wanted to tell you that you can use double dollar i.e.  to trigger the displaymode, this makes your answer look beautiful. Also, you can use \rleft( and \right) for brackets to adjust there size according to their content. – Jaideep Khare Apr 27 '17 at 10:57