2. In a particular prison, 60% of the population are hardened criminals, 50% are

ID: 3040709 • Letter: 2

Question

2. In a particular prison, 60% of the population are hardened criminals, 50% are serving terms longer than five years, and 40% are hardened criminals serving a term longer than five years. If a prisoner is selected at random, find the probability that the prisoner is (a) a hardened criminal if you know the prisoner’s term is ten years; (b) serving a term longer than five years if the prisoner is a hardened criminal; (c) not a hardened criminal if the prisoner is serving a term of ten years. 2. In a particular prison, 60% of the population are hardened criminals, 50% are serving terms longer than five years, and 40% are hardened criminals serving a term longer than five years. If a prisoner is selected at random, find the probability that the prisoner is (a) a hardened criminal if you know the prisoner’s term is ten years; (b) serving a term longer than five years if the prisoner is a hardened criminal; (c) not a hardened criminal if the prisoner is serving a term of ten years. 2. In a particular prison, 60% of the population are hardened criminals, 50% are serving terms longer than five years, and 40% are hardened criminals serving a term longer than five years. If a prisoner is selected at random, find the probability that the prisoner is (a) a hardened criminal if you know the prisoner’s term is ten years; (b) serving a term longer than five years if the prisoner is a hardened criminal; (c) not a hardened criminal if the prisoner is serving a term of ten years.

Explanation / Answer

a) We need to calculate

P( hardened criminal/prisoner’s term is ten years)

= 0.40

b) P( serving a term longer than five years/prisoner is a hardened criminal)

= (0.40*0.50)/0.60

= 0.33

c) P( Not a hardened criminal /prisoner is serving a term of ten years)

= 1-0.40

= 0.60

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2. In a particular prison, 60% of the population are hardened criminals, 50% are

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