Question

1. The following table shows some results from an analysis by the ABC (Australian Broadcasting Corporation) in April 2017 on property ownership of Australian politicians. It lists the num- ber of politicians in each of the major party groups/coalitions and whether or not they have a property specifically listed as investment property (IP for short). owns IP 42 Labor/Greens Liberal/National/LNP other doesn't own IP 63 47 14 124 105 105 14 100 224 A politician is chosen at random from this group. Let P de- note the event they have an investment property, LN denote the event they are are a Lib/Nat/LNP member, LG denote the event they are a Labor/Greens member and O denote the event they are a other party member (minor parties and inde- pendents). Determine each of the following and describe the event in words. (a) Pr(PC) (b) Pr(LG) (c) Pr(PCLN) (d) Pr(P|LG)

Also please do probability of (e) Pr(O|P^c).
Please provide solutions calculation steps showing formula and short explanation text.

Answer 1

(a)

P : Event they have an investment property

P^c : Event they do not have an investment property

Pr( P^c ) = Probability that a randomly chosen politician does not own an investment property   

=  Number of politicians who doesn't own IP / Total number politicians = 124/224 = 31/56

Pr( P^c ) = 31/56

(b)

LG : Event they are labor/green members

Pr (LG) = Probability that a randomly chosen politician is labor/green members

= Number of politicians who are labor/green members / Total number politicians = 105/224

Pr (LG) = 105/224

(c)

P^c : Event they do not have an investment property

LN : Event they are liberal/national/NLP members

Pr (P^c | LN) = Probability that a randomly chosen politician does not own an investment property given that the chosen politician is a liberal/national/NLP member

= Number of liberal/national/NLP members who does not own an investment property / Number of liberal/national/NLP members

= 47/105

Pr (P^c | LN) = 47/105

(d)

P : Event they have an investment property

LG : Event they are labor/green members

Pr (P | LG) = Probability that a randomly chosen politician own an investment property given that the chosen politician is a Labor/Greens

= Number of Labor/Greens members who own an investment property / Number of Labor/Greens members

= 42/105

Pr (P | LG) = 42/105

(e)

O : Event they are other

P^c : Event they do not have an investment property

P(O|P^c) = Probability that a randomly chosen politician is an other member given that the chosen politician does not own a property

= Number of politicians who does not own a property and are other / Total number of politicians who does not own a property

= 14/124 = 7/62

P(O|P^c) = 7/62