Its absolutely awesome that you took some time out to actually have a look at the questions.
Lets break down the question and hopefully set you on the right track.
Question 4A and Question 4B are somewhat linked. It is therefore crucial that you first understand the underlying idea of Question 4A before answering Question 4B.
The minining company sets up a risk pool to fund death benefits for the miners' families.They will all contribute annually to the pool and the total annual contributions equal the expected cost of the death beneﬁts for that year. If a miner dies on the job, their dependents get a beneﬁt equal to 2 times the miner’s annual salary. There are 500 000 miners in the company.
Essentially the idea of this question is to find the average amount to be contributed by each worker to the fund. This average amount that all miners will contribute should be enough to cover the expected cost of deaths benefits ( these are payments made from the fund out to beneficiaries on the death of a policyholder ) to be paid to the families of the miners who die. So the word "pool" actually serves a great purpose here, because you essentially have to think of all the deaths benefits to be paid out as some sort of pool. The total value of the pool should then be funded by the miners, each paying the same amount( "an equal slice of the pie") to make up the total value of the pool. The Actuarial question of interest should then be : What is the total amount of the death benefits that will then be used to determine the amount that each miner should contribute. The question then says that "If a miner dies on the job, their dependents get a beneﬁt equal to 2 times the miner’s annual salary". We are furthermore given the chance of death of a miner for each category. So the formula you should use should take something of the form :
EPV(Benefits) = 2 x prob(death) x Annual Salary.
Note the complexity however, you are given different categories of miners with different probabilities relating to each category. There are at least two ways to get around this : Do a separate EPV(Benefits) calculation for each category , finding the total for all miners in that category and then add the EPV(Benefits) amounts for all categories and divide by the total amount of all workers . This will give you the amount to be paid by each miner. The other approach is to use weighted averages based on number of workers in each category, where the probabilities in the categories with the highest number of workers will contribute most and vice versa. The latter is slightly less obvious but essentially does the same thing as the first method.
Question 4B is simply a continuation of question 4A.Essentially Question 4B is asking what percentage(%) of the total value of all the salaries combined will be used to cover the total death benefits. Like the previous question, there are inherently many ways to compute this percentage. One obvious way would be to simply take the total amount of death benefits to be paid and dividing it by the total salaries of all miners( and multiplying by 100 to make it a % of course).
I hope this helped.
This was a tut test and you should attempt to do it on your own. Please check the answers with your tutor in the next tutorial or post your attempt here and we will then chat through it.