SOLUTION: If p(a)= .6, p(b)= .22, and p(a and b)= .31 . Find p(a and b)

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Question 1178818: If p(a)= .6, p(b)= .22, and p(a and b)= .31 . Find p(a and b)
Found 2 solutions by MathLover1, ikleyn:
Answer by MathLover1(20850)   (Show Source): You can put this solution on YOUR website!

given:
, , and ( and )=.
Find ( and )-> doesn't make sense, it's already given
assuming you need to find ( or ), use
General Addition Rule

( or ) = - ( and )
( or ) =
( or ) =


Answer by ikleyn(52857)   (Show Source): You can put this solution on YOUR website!
.
If p(a)= .6, p(b)= .22, and p(a and b)= .31 . Find p(a and b)
~~~~~~~~~~~~~~



            This post has  SEVERAL  FATAL  ERRORS,  that make it  FATALLY  NONSENSICAL. 



First error is that  p(a and b) is given,  "p(a and b)= .31.",  and then the problem asks again about the value of p(a and b).


@MathLover1 sees it and makes an assumption that the problem should ask about p(a or b).



But it is not possible to have  p(a) = 0.6, p(b) = 0.22 and p(a and b) = 0.31:


    +------------------------------------------------------------------+
    |    with given p(a) and p(b),  p(a and b) MUST BE less or equal   |
    |    the minimum of both values p(a) = 0.6 and p(b) = 0.22.        |
    +------------------------------------------------------------------+


It is the second fatal error of the post and of the @MathLover1 solution.



THERFORE


    NEITHER the given data in the post makes sense

    NOR the "solution" by @MathLover1 makes sense.

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

The conclusion and a medical/mathematical  DIAGNOSIS  is that

            the given post/(the problem)/(the solution by @MathLover1)
            are all good only to throw all this stuff to the  TRASH  BIN.


////////////


Another conclusion and the diagnosis is that both the problem's composer and @Matlover1 are unfamiliar
with elementary basic properties of probabilities.



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