SOLUTION: In a certain federal prison it is known that 2/3 of the inmates are under 25 years of age. It is also known that 3/5 of the inmates are male and the 5/8 of the inmates are female o

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Question 252540: In a certain federal prison it is known that 2/3 of the inmates are under 25 years of age. It is also known that 3/5 of the inmates are male and the 5/8 of the inmates are female or 25 years of age or older. What is the probability that a prisoner selected at random from this prison is female and at least 25 years old?
Found 2 solutions by stanbon, edjones:
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
In a certain federal prison it is known that 2/3 of the inmates are under 25 years of age. It is also known that 3/5 of the inmates are male and the 5/8 of the inmates are female or 25 years of age or older. What is the probability that a prisoner selected at random from this prison is female and at least 25 years old?
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P(F and >=25) = P(F)+P(>=25)-P(F or >=25)
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= (1-(3/5))+(1-(2/3))-(5/8)
= (2/5)+(1/3)-(5/8)
= (24+40-15)/120
= 49/120
= 0.4083..
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Cheers,
Stan H.

Answer by edjones(8007) (Show Source):
You can put this solution on YOUR website!
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.
.
Ed
.