SOLUTION: Events A and B are dependent. P(A)= 5/12 and P(B given A) = 6/11. Find P(A and B). Appreciate the help :D

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Question 1174251: Events A and B are dependent. P(A)= 5/12
and P(B given A) = 6/11. Find P(A and B).
Appreciate the help :D
Found 3 solutions by ikleyn, Theo, MathTherapy:
Answer by ikleyn(52788)   (Show Source): You can put this solution on YOUR website!
.
Events A and B are dependent. P(A)= 5/12
and P(B given A) = 6/11. Find P(A and B).
~~~~~~~~~~~~~ 


P(B given A) is the conditional probability.


The standard classical designation for it is  P(B|A).


So, P(B given A) is the same as  P(B|A).


By the definition,  P(B|A) = P(B ∩ A) / P(A).


So, you are  GIVEN  that   


    P(B ∩ A) / P(A) = ,   or,  which is the same,

    P(B ∩ A) :  = .


THEREFORE,

    P(B ∩ A) =  =  = .    ANSWER

Solved.

-----------------

In this site, there are two lessons for problems on conditional probability. They are
    - Conditional probability problems
    - Conditional probability problems REVISITED

Read them to develop your skills and knowledge.

Also,  you have this free of charge online textbook in ALGEBRA-II in this site
    - ALGEBRA-II - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic  "Solved problems on Probability"
and  "Additional problems on Probability".


Save the link to this textbook together with its description

Free of charge online textbook in ALGEBRA-II
https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson

into your archive and use when it is needed.



Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
p(b given a) = p(a and b) / p(a)

you have p(a) = 5/12 and you have p(b given a) = 6/11.

formula becomes 6/11 = p(a and b) / (5/12)

multiply both sides of this equation by (5/12) to get:
(6/11) * (5/12) = p(a and b).
simplify to get 30/132 = p(a and b).
simplify further to get 5/22 = p(a and b)

your solution is p(a and b) = 5/22.

confirm by replacing p(a and b) in the original equation to get:

p(b given a) = p(a and b) / p(a) becomes 6/11 = 5/22 / (5/12).
this becomes 6/11 = 5/22 * 12/5 which becomes 6/11 = 12/22.
simplify to get 6/11 = 6/11 which is true.
this confirms the value of p(a and b) is good.








Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!

Events A and B are dependent. P(A)= 5/12
and P(B given A) = 6/11. Find P(A and B).
Appreciate the help :D


      ------- Substituting 

 ---- Cross-multiplying



 

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