Question 252540
For this problem old means 25 or older and F means female.
Refer to the Venn diagram below.
2/5 are female, the entire red circle.
1/3 are old,  the entire green circle
5/8 are F or old. This is a union of the red and green circles and includes the intersection of the circles.
Let the intersection of the circles be x.
The red circle left of the intersection is 2/5 - x.
The green circle to the right of the intersection is 1/3 - x.
.
(2/5 - x) + (1/3 - x) + x = 5/8
-x + 11/15 = 5/8
-x=-13/120
x=.1083... Probability prisoner selected at random is F and old.

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Ed
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{{{drawing( 300, 300, -5, 5, -5, 5,
  rectangle( -4.5, 4.5, 4.5, -3.5 ),
red( circle(- 1.5, 0, 2.5) ),
  green( circle( 2, 0, 2.25 ) ))}}}