Question 1180354
For two events A and B, P(A) = 0.3 and P(B)=0.2. (a) If A and B are independent, then P(A|B) =
P(A∩B) =
P(A∪B) =
(b) If A and B are dependent and P(A|B) = 0.25,
then P(B|A) =
P(A∩B) =
~~~~~~~~~~~~~~~~~~~



                    I will solve part  a),  ONLY.



I will answer in other, more natural order.



<pre>
First, P(A ∩ B) = P(A)*P(B) = 0.3*0.2 = 0.06  (since A and B are independent).


Second,  P(A U B) = P(A) + P(B) - P(A ∩ B) = 0.3 + 0.2 - 0.06 = 0.44.


Third, P(A | B) = {{{P(A_intersection_B)/P(B)}}} = {{{0.06/0.2}}} = 0.3.
</pre>

Solved.



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Edwin expressed &nbsp;"a favor" &nbsp;in my address - - - so, &nbsp;I will express my favor in his address,&nbsp; mutually.


Ignore his solution: &nbsp;it is &nbsp;INCORRECT:


    &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;It is incorrect, because it is based on your incorrect formulation of the part &nbsp;b).


    &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;The event &nbsp;A &nbsp;and &nbsp;B &nbsp;must be &nbsp;INDEPENDENT - - - while your formulation 

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;calls them &nbsp;"DEPENDENT" &nbsp;- - - &nbsp;clearly, &nbsp;directly, &nbsp;explicitly and incorrectly.



&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;And &nbsp;Edwin &nbsp;NEITHER &nbsp;disproved &nbsp;NOR &nbsp;corrected it . . .