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?
Select:  A) 0.1591  B) 0.2727  C) 0.375  D) 0.2767  E) None of these
Explanation :   The percentage of three different types of policy holders and the corresponding probability of dying in the next 1 year are as follow :   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.   =&gt;T×(50×0.01/100)+(30×0.008/100)+(20×0.007/100).   =&gt;T×(0.88/100).   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 :-   =&gt;((30x0.88xT)/100)/ (Tx(0.88/100)).   =&gt;24/88.   =&gt;3/11.   =&gt;0.2727.   Answer : 0.2727
<result>B</result>
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?