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A married couple purchases two insurance policies with single premium for each policies and the benefit is 12,000 if death occurs within policy years which will end after ten years. If the probabilities of

  • Only the wife to live at least within policy years is 2.5%
  • Only the husband to live at least within policy years is 3.6%
  • Both of them are alive at least within policy years is 86.4%

Calculate the difference between the premium paid and the expected claim if it's known the husband is still alive at least within policy years.

a) 480$\qquad$ b) -11,000$\qquad$ c) 360$\qquad$ d) 520$\qquad$ e) None is correct


Here we know the premium paid will be $2\times500=1,000$ and the expected claim if it's known the husband is still alive at least within policy years is $3.6\%\times12,000=432$. So, the difference will be $1,000-432=568$ and the answer should be e) None is correct, but the key answer of this problem is 520. Where did I make mistake?

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  • $\begingroup$ How do you calculate the premium paid? $\endgroup$ – Jimmy R. Nov 10 '15 at 13:12
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You're asked to calculate the difference "if it's known the husband is still alive".

The husband will still be alive 3.6% + 86.4% = 90% of the time. In that scenario, the wife dies with probability 3.6%/90%.

1000 - 3.6/90 * 12000 = 1000 - 480 = 520.

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  • $\begingroup$ Can you elaborate why the wife dies with probability 3.6%/90%? Thanks! $\endgroup$ – Richard Aleint Nov 10 '15 at 13:22
  • $\begingroup$ It's the conditional probability. We are only interested in the 90% of cases where the husband lives. That is made up of 3.6% where the wife dies, and 86.4% where she doesn't. Proportionally the wife dies in 3.6/90 of those cases. $\endgroup$ – Neil W Nov 10 '15 at 13:40

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