# Difficult Probability Solved QuestionAptitude Discussion

 Q. 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?
 ✖ A. 0.1591 ✔ B. 0.2727 ✖ C. 0.375 ✖ D. None of these

Solution:
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:

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

$=\dfrac{24}{88}$

$=\dfrac{3}{11}$

$=0.2727$

## (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

Sandy
()

hi sir i have a small question give the ans plz

4 boys and 2 girls in 1 row 2 boys and 1 girls in 2 row ,5 boys and 3 girls in 3 rd row if a girl laughed what is the propabability that the girl who laughed loudly was from 3rd row