In the electorate of Wobbegong, 60% of the electors are male, and 40% female, 55
ID: 3177909 • Letter: I
Question
In the electorate of Wobbegong, 60% of the electors are male, and 40% female, 55% of the males vote Labor 40% Liberal and 5% Other, while 45% of the females vote Labor, 50% Liberal and 5% Other. A Labor voter is chosen at random. What is the probability that the voter is male? (b) A Department of Health report states: if a tested patient has the disease, then the test will indicate positive' 99% of the time: and if a tested patient does not have the disease, then the test will indicate 'negative' 95% of the time. Supposing that only one in a thousand of the population has that disease, calculate the probability that the tested patient has the disease given that the test was positive. Supposing that only one in a thousand of the population has that disease, calculate the probability that the tested patient has the disease given that the test was negative.Explanation / Answer
The follwoing table is from the given information
A Labor voter is choosen at random, What is the probability that the voter is male
Probability that the voter is male given that a Labor voter is choosen
= Number of Male voter who voted for Labor / Number of Labor voters
From the table ,
Number of Male voter who voted for Labor = 33
Number of Labor Voters =51
Probability that the voter is male given that a Labor voter is choosen = 33/51
Male Female Total Labor (55x60)/100 =33 (45x40)/100 =18 33+18=51 Liberal (40x60)/100=24 (50x40)/100=20 24+20=44 Others (5x60)/100 =3 (5x40)/100 =2 3+2=5 Total 60 40