Question 1095453
<pre><font size=4><b>
Let x,y,z, and w be the probabilities of the 4 regions
in the Venn diagram below:

{{{drawing(300,200,-4,4,-2,4.8,rectangle(-4,-1.6,4,4.4), locate(-2,1.8,x),locate(1.5,1.7,z),locate(-3.7,-1,w), locate(-3.6,2.5,A), locate(-.1,1.8,y),red(circle(-sqrt(2),sqrt(2),2)),red(circle(-sqrt(2),sqrt(2),1.95)),red(circle(-sqrt(2),sqrt(2),1.975)),
blue(circle(sqrt(2),sqrt(2),2),circle(sqrt(2),sqrt(2),1.95),circle(sqrt(2),sqrt(2),1.975)),
locate(3.4,2.5,B)
 )}}}

P(A) = x+y = 0.3
P(B) = y+z = 0.6
P(A&B') = x = 0.1
P(AUB) = x+y+z = ??

Since x = 0.1,

substitute 0.1 for x in x+y = 0.3
                      0.1+y = 0.3
                          y = 0.2

Substitute 0.2 for y in y+z = 0.6
                      0.2+z = 0.6
                          z = 0.4

 P(AUB) = x+y+z = 0.1+0.2+0.4 = 0.7   <--answer

It's also true that w = P(A'&B') = 1 - 0.7 = 0.3


{{{drawing(300,200,-4,4,-2,4.8,rectangle(-4,-1.6,4,4.4), locate(-2,1.8,0.1),locate(1.5,1.7,0.4),locate(-3.7,-1,0.3), locate(-3.6,2.5,A), locate(-.2,1.8,0.2),red(circle(-sqrt(2),sqrt(2),2)),red(circle(-sqrt(2),sqrt(2),1.95)),red(circle(-sqrt(2),sqrt(2),1.975)),
blue(circle(sqrt(2),sqrt(2),2),circle(sqrt(2),sqrt(2),1.95),circle(sqrt(2),sqrt(2),1.975)),
locate(3.4,2.5,B)
 )}}}

Edwin</pre></b></font>