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Thread: SOA Sample question 113.

  1. #1
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    SOA Sample question 113.

    Two life insurance policies, each with a death benefit of 10, 000 and a one-time premium
    of 500, are sold to a couple, one for each person. The policies will expire at the end of the
    tenth year. The probability that only the wife will survive at least ten years is 0.025, the
    probability that only the husband will survive at least ten years is 0.01, and the probability
    that both of them will survive at least ten years is 0.96. What is the expected excess of
    premiums over claims, given that the husband survives at least ten years?

    I have looked at the solutions and wondered where in the question that says that couples won't get a dime from the insurance company if both of them survive at least 10 years? And they never use the 0.025 in the answer this can throw one off balance.
    Last edited by Dabsy; June 18th 2013 at 12:56 AM.

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    Quote Originally Posted by Dabsy View Post
    Two life insurance policies, each with a death benefit of 10, 000 and a one-time premium
    of 500, are sold to a couple, one for each person. The policies will expire at the end of the
    tenth year. The probability that only the wife will survive at least ten years is 0.025, the
    probability that only the husband will survive at least ten years is 0.01, and the probability
    that both of them will survive at least ten years is 0.96. What is the expected excess of
    premiums over claims, given that the husband survives at least ten years?

    I have looked at the solutions and wondered where in the question that says that couples won't get a dime from the insurance company if both of them survive at least 10 years? And they never use the 0.025 in the answer this can throw one off balance.
    It is because these are life insurance policies which pay benefit when someone is dead.

    Is English your secondary language? Anyway, you may need to improve at least one of the followings: language skill and common sense.

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    Hey, you need to watch you language,you're not obliged to respond to a question posted in this room.You got common sense,right, and you got skill. Absolute bunkum.
    Last edited by Dabsy; June 21st 2013 at 03:10 PM.

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    Quote Originally Posted by Dabsy View Post
    Hey, you need to watch you language,you're not obliged to respond to a question posted in this room.You got common sense,right, and you got skill. Absolute bunkum.
    What was wrong with his language? He didn't curse and he used proper spelling and grammar.

    At the very least he didn't start three threads asking the same question

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    Hey, even if you're the moderator, you have no control over my postings. You're too arrogant for nothing.Get real, my friend.

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    I'm pretty sure, you're a sad dimwit, who thinks can bully people in the chat room.Get something else to do if you're bored.I have over the time watched how you displayed your nonchalant attitude.People like you are nothing but rascals who should never be minded.All your life your best achievement is to be a postmaster ,I don't bloody care.Whatever you think you're and you cannot teach me English period
    Last edited by Dabsy; June 21st 2013 at 05:56 PM.

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    Quote Originally Posted by Dabsy View Post
    Hey, even if you're the moderator, you have no control over my postings. You're too arrogant for nothing.Get real, my friend.
    1) I am not a moderator nor did I ever claim to control your "postings". I was simply pointing out that whatever BeanCounter said to you, he at least follows posting etiquette in not posting the same question 3 times. In a row. Within 24 hours.

    2) A moderator CAN delete your POSTS so yes a moderator does have "control over your postings".

    3) Please show me how I am arrogant in my replies to you.

    4) I am real, but not your friend

  8. #8
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    Quote Originally Posted by Dabsy View Post
    I'm pretty sure, you're a sad dimwit, who thinks can bully people in the chat room.Get something else to do if you're bored.I have over the time watched how you displayed your nonchalant attitude.People like you are nothing but rascals who should never be minded.All your life your best achievement is to be a postmaster ,I don't bloody care.Whatever you think you're and you cannot teach me English period
    1) See, now you're being insulting.

    2) And this is not a chat room.

    3) I'm a rascal? Which one? Alfalfa?!

    4) I'm not a postmaster (in fact not affiliated in any way with U.S. mail).

    5) I wasn't trying to teach you English. Such a task is not for me. All BeanCounter was trying to point out to you is that you NEED to learn English better if you hope to pass these exams.

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    Silence is the best answer to a ... especially one acting like a demigod.If you don't know what my friend in this context means, get your idiomatic expression back to life. Your best friend is nothing but the computer.So, I can't be your friend.
    Last edited by Dabsy; June 21st 2013 at 07:11 PM.

  10. #10
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    For your first question, I think the implication is that the policy is a simple term 10 that has no return of premium riders or any other frills such as participating dividends paid to the client, etc.. Rule of thumb is that you try not to complicate things too much.

    For your second question, the .025 probability isn't all that important. We don't care about the probability if the husband dies and the wife survives.

    P(X) * P(~Y) = .025
    P(~X) * P(Y) = .01
    P(X) * P(Y) = .96

    .97 = .96 + .01 = P(Y)P(X) + P(Y)P(~X) = P(Y) [P(X) + P(~X)] = P(Y).

    P(X|Y) = P(X∩Y)/P(Y) = .96/.97 = .9897

    Premium is 1000.

    Expected losses are 10000 (1 - .9897) = 103.

    1000 – 103 = 897 is the expected excess premium.

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