Question

1. Consider the following proportions regarding age and type of offence.

	Type of Offence
Age (Years)	Violent	Property	Drug
10 – 19	0.02	0.02	0.08
20 – 29	0.05	0.04	0.11
30 – 39	0.04	0.02	0.08
40 – 49	0.03	0.04	0.09
50 – 59	0.04	0.06	0.05
60 – 69	0.01	0.06	0.04
70 – 79	0.01	0.03	0.03
80 – 89	0.00	0.03	0.02

1. What is the probability of being aged 20 to 29 years?
2. What is the probability of having committed a violent offence?
3. What is the probability of being aged 30 to 69 years?
4. What is the probability of being aged 40 to 49 years given a property offence?
5. What is the probability of a violent or drug offence given an age of 20 to 29 years?

Answer 1

Age (Years)	Violent	Property	Drug	total
10 – 19	0.02	0.02	0.08	0.12
20 – 29	0.05	0.04	0.11	0.2
30 – 39	0.04	0.02	0.08	0.14
40 – 49	0.03	0.04	0.09	0.16
50 – 59	0.04	0.06	0.05	0.15
60 – 69	0.01	0.06	0.04	0.11
70 – 79	0.01	0.03	0.03	0.07
80 – 89	0	0.03	0.02	0.05
total	0.2	0.3	0.5	1

a)

probability of being aged 20 to 29 years =0.05+0.04+0.11 =0.20

b)

probability of having committed a violent offence =0.02+0.05+0.04+0.03+0.04+0.01+0.01+0 =0.2

c)

probability of being aged 30 to 69 years =P(30-39)+P(40-49)+P(50-59)+P(60-69)

=0.14+0.16+0.15+0.11 =0.56

d)

P(40-49 | property offence) =P(40-49 and property offence)/P(property offence)=0.02/0.14 =0.1429

e)

P(Violent or drug offence |20-29 years )=(0.05+0.11)/0.2 =0.8