Combined Probability P ( A ) 2 3 , P ( A | B ) = 1 3 and P ( A ∪ B ) = 4 5 .Find P(B).I honestly have no idea how to even approach this problem, as I cannot find any helpful online notes on Combined probability. For instance, I don't even know how to find P(A ⋂ B) if given P(A ∪ B), P(A) and P(B).So how would I solve a simple problem like finding P(A ⋂ B), and then how would I use this knowledge to solve the question mentioned above?

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Combined Probability  P  (  A  )      2    3    ,  P  (  A      |    B  )  =      1    3  and  P  (  A  ∪  B  )  =      4    5    .Find P(B).I honestly have no idea how to even approach this problem, as I cannot find any helpful online notes on Combined probability. For instance, I don&#039;t even know how to find P(A ⋂ B) if given P(A ∪ B), P(A) and P(B).So how would I solve a simple problem like finding P(A ⋂ B), and then how would I use this knowledge to solve the question mentioned above?

Tyree Duke · Accepted Answer

You don&#039;t need to find   P  (  A  ∩  B  ), but you can use the knowledge that   P  (  A  ∩  B  )  =  P  (  A      |    B  )  ×  P  (  B  )By the Inclusion-Exclusion principle:  P  (  A  ∪  B  )  =  P  (  A  )  +  P  (  B  )  −  P  (  A  ∩  B  )      4    5    =      2    3    +  P  (  B  )  −  P  (  A  ∩  B  )But   P  (  A  ∩  B  )  =  P  (  A      |    B  )  ×  P  (  B  )So       4    5    −      2    3    =  P  (  B  )  −  P  (  A      |    B  )  ×  P  (  B  )We know   P  (  A      |    B  )      2    15    =  P  (  B  )  (  1  −      1    3    )  P  (  B  )  =      1    5

Combined Probability P ( A ) 2 3 </mfrac> , P ( A <mro

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