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Sun Life Insurance company issues standard, preferred and ultra-preferred policies. Among the company's policy holders of a certain age, $50%$ are standard with the probability of 0.01 dying in the next year, $30%$ are preferred with a probability of 0.008 of dying in the next year and $20%$ are ultra-preferred with a probability of 0.007 of dying in the next year. If a policy holder of that age dies in the next year, what is the probability of the decreased being a preferred policy holder?








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Option(B) is correct

The percentage of three different types of policy holders and the corresponding probability of dying in the next 1 year are as follow :

Table below can be scrolled horizontally

Type Standard Preferred Ultra-Preferred
Percentage 50 30 20
Probability 0.01 0.008 0.007


The expected number of deaths among all the policy holders of the given age [say $P$] during the next year.

\(=T\times \left(\dfrac{50\times 0.01}{100}+\dfrac{30\times 0.008}{100}+\dfrac{20\times 0.007}{100}\right)\)

\(=T\times \left(\dfrac{0.88}{100}\right)\)

Where T= Total number of policy holder of age $P$

If any of these policy holders (who die during the next year) is picked at random, the probability that he is a preferred policy holder is:

\(= \left(\dfrac{\left(\dfrac{30\times 0.88\times T}{100}\right)}{T\times \left(\dfrac{0.88}{100}\right)}\right)\)




(2) Comment(s)

Ross F

There is a typo in the solution,

The numerator is written 30x0.88xT, It should be 30x0.008xT

This gives you the correct fraction and is the actual probability


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