Question

The table below classifies residents of a regional area of New South Wales by gender and age.

Age groups	Males	Females	Persons
0-4 years	410	369	779
5-14 years	952	861	1,813
15-19 years	478	501	979
20-24 years	594	559	1,153
25-34 years	859	885	1,744
35-44 years	886	974	1,860
45-54 years	1,026	1,105	2,131
55-64 years	1,097	1,033	2,130
65-74 years	677	703	1,380
75-84 years	333	492	825
85 years and over	154	327	481
Total	7,466	7,809	15,275

1. If a resident is chosen at random, what is the probability that the resident:
   1. is male?
   2. is a female aged at least 65 years?
   3. is a child aged under 15 years?
2. What proportion of children, defined as under 15 years of age, are male?

3. If a resident is chosen at random, are the events ’Child under 15’ and ’Male’ independent?

4. What is the probability that a female resident chosen at random is at least 65 years of age?

Answer 1

a)

i)probability that the resident is male =7466/15275=0.4888

ii)P(is a female aged at least 65 years)=(703+492+327)/15275=0.0996

iii) P(a child aged under 15 years) =(779+1813)/15275 =0.1697

b)

P(male |under 15) =(410+952)/(779+1813)=0.5255

a)

since P(male ) =0.4888 is not equal to P(male |under 15) =0.5255 , evenrts   ’Child under 15’ and ’Male’ are not independent

b)probability that a female resident chosen at random is at least 65 years of age

=(703+492+327)/7809

=0.1949