Answer to Question #205145 in Statistics and Probability for Shema Derrick

Question #205145

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 that 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?


1
Expert's answer
2021-06-16T17:19:16-0400

Let AA denotes the event "inmate is under 25 years of age".

Let MM denotes the event "inmate is a male".

Let FF denotes the event "inmate is a female".

Given P(A)=23,P(M)=35,P(FA)=58.P(A)=\dfrac{2}{3}, P(M)=\dfrac{3}{5}, P(F\cup A')=\dfrac{5}{8}.


P(A)=1P(A)=123=13P(A')=1-P(A)=1-\dfrac{2}{3}=\dfrac{1}{3}

P(F)=1P(M)=135=25P(F)=1-P(M)=1-\dfrac{3}{5}=\dfrac{2}{5}


P(FA)=P(F)+P(A)P(FA)P(F\cap A')=P(F)+P(A')-P(F\cup A')

P(FA)=25+1358=48+4075120P(F\cap A')=\dfrac{2}{5}+\dfrac{1}{3}-\dfrac{5}{8}=\dfrac{48+40-75}{120}

=13120=\dfrac{13}{120}


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