Question 1 (10 marks] (a) In the electorate of Wobbegong, 60% of the electors ar

Question

Question 1 (10 marks] (a) 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 female? (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.

Explanation / Answer

a)P(Labor)=P(male and labor)+P(female and labor)=0.6*0.55+0.4*0.45=0.51

hence P(female|Voter)=P(female and labor)/P(female)=0.4*0.45/0.51=0.3529

b)

P(test positive)=P(has disease and test positive)+P(not has disease and test positive)

=(1/1000)*0.99+(1-1/1000)*(1-0.95)=0.05094

hence P(has disease|test positive)=P(has disease and test positive)/P(test positive)=(1/1000)*0.99/0.05094

=0.0194

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