Question 1089429
Let E and F be two mutually exclusive events and suppose P(E) = 0.4 and P(F) = 0.2. Compute the probabilities below.
<pre>
Draw the Venn diagram.  Since E and F are mutually exclusive, they
do not overlap.  The rectangle represents the entire sample space,
which has probability 1.  Therefore the region outside the regions E
and F must have probability 0.4, so that all three regions will have
probability 1, which means that all three probabilities must total 1.

{{{drawing(400,8400/41,-4.1,4.1,-2.1,2.1,
locate(-2,1.78,E), locate(2,1.78,F),locate(2,0,0.2),locate(-2,0,0.4),
line(-4,-2,4,-2),line(4,-2,4,2),
line(4,2,-4,2), locate(0,-1.3,0.4),
line(-4,2,-4,-2),  circle(2,0,1.5), circle(-2,0,1.5) )}}}
</pre>
(a) P(E intersection F).<pre>That's the probability of where the circle 
overlap.  Since they do not overlap, the probability is 0. 
</pre>  
(b) P(E union F).<pre>That's the probability of being in either of the
two circles, which is 0.4+0.2 = 0.6   
</pre>  
(c) P(Ec).<pre>That's the probability of not being inside the left circle, which is either 
gotten by 1-0.4 = 0.6 or by adding the two probabilities
not including the left circle which is 0.4+0.2 = 0.6  
</pre>  
(d) P(Ec intersection Fc).<pre>That's the probability of not being in E and not being in F, which means being 
outside both circles.  So the probability is 0.4. 

Edwin</pre>