Sun Life Insurance Company issues standard,preferred, and ultra-preferred policies. Amongthe company’s policy holders of a certain age,50% are standard with a probability of 0.01 ofdying in the next year, 30% are preferred with aprobability 0.008 of dying in the next year, and20% are ultra-preferred with a probability of0.007 of dying in the next year. If a policy holderof that age dies in the next year, what is theprobability of the deceased being a preferredpolicy holder?

If there are 10000 policy holders then 5000 are of standard, 3000 are of preferred and 2000 are of ultra-preferred

0.01 of standard policy holders may die next year i.e. 50 of standard policy holder may die next year

0.008 of preferred policy holders may die next year i.e. 24 of preferred policy holders may die next year

0.007 of ultra-preferred policy holders may die next year i.e. 14 of ultra-preferred policy holders may die next year

Total number of people that may die next year = 50+24+14 = 88

Probability that the person died is a preferred policy holder is $$\frac{24}{88}$$ = 0.2727

Therefore our answer is option 'B'