Example Question

[Alele]

Hi guys,

I came across this question when revising for the coming CT3 exam. Would a question like this appear in the IFoA exams and if so, how many marks do you think it's worth?

The reason for this question is because there are 2 very different methods that could be applied to find the answer. One of the methods involves drawing a table and filling it out by general reasoning which requires minimal written calculation. This method is very short and quick. The second method is much longer and is a step by step method that applies the law of total probability and would take about 5-10 minutes. Hence I was wondering whether this question would be awarded enough marks to warrant using the much longer method that would make it possible to earn method marks in case of any calculation errors unlike the first method.

An actuary is studying the prevalence of three health risk factors, denoted
by A;B; and C; within a population of women. For each of the three factors,
the probability is \(0.1\) that a woman in the population has only this risk factor
(and no others). For any two of the three factors, the probability is \(0.12\) that
she has exactly these two risk factors (but not the other). The probability
that a woman has all three risk factors, given that she has A and B, is \(\frac{1}{3}\) :
What is the probability that a woman has none of the three risk factors,
given that she does not have risk factor A?

 

[John Lee]

An actuary is studying the prevalence of three health risk factors, denoted
by A;B; and C; within a population of women. For each of the three factors,
the probability is \(0.1\) that a woman in the population has only this risk factor
(and no others). For any two of the three factors, the probability is \(0.12\) that
she has exactly these two risk factors (but not the other). The probability
that a woman has all three risk factors, given that she has A and B, is \(\frac{1}{3}\) :
What is the probability that a woman has none of the three risk factors,
given that she does not have risk factor A?

Since it's a "calculate" question you can do it any valid method. So I'd go for the quick one - and as long as you include your table or venn diagram then you should get working marks if the answer is wrong.

 

[Alele]

Since it's a "calculate" question you can do it any valid method. So I'd go for the quick one - and as long as you include your table or venn diagram then you should get working marks if the answer is wrong.

Thanks John. How many marks would this question be worth in your opinion?

 

[John Lee]

Thanks John. How many marks would this question be worth in your opinion?

Hmmm, 3 marks (or 5 if they're feeling generous).

So 5.4-9 minutes of time.