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Law of total probability

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  • Law of total probability

    An insurance company offers one of the following choices to each of their employees:
    (i) Take exactly two insurances
    (ii) Take no insurance but get a lump sum of money
    The probability of having automobile insurance is 62.5%. The probability of having life insurance is 37.5%. The probability of having homeowners insurance is 25%. What is the probability of people who picked life insurance and homeowners insurance?


    I got that the answer is 0, but the source says that the answer is 0.125 (by solving this using the law of total probability three times). Is there a typo?
    Does anyone agree my answer of 0, or did I make a mistake?

    I hope someone can confirm this. Thanks!

  • #2
    Is this how you did it?

    x+y = .625
    y+z = .375
    x+z = .25

    x+y+z = .625

    so z = 0.
    I also get 0

    Comment


    • #3
      Originally posted by weezy View Post
      Is this how you did it?

      x+y = .625
      y+z = .375
      x+z = .25

      x+y+z = .625

      so z = 0.
      I also get 0
      Yes.

      y+z = .375
      x+z = .25

      So x+y+2z=0.625
      =>2z=0
      =>z=0

      So I think the answer is indeed 0.
      Thanks!

      Comment


      • #4
        Why are you saying x + y = .625, granted it's true that 2 have to be selected but what makes you think it's those 2

        Comment


        • #5
          A google search shows that the homeowner's is 50%.

          An insurance company offers one of the following choices to each of their employees:
          (i) Take exactly two insurances
          (ii) Take no insurance but get a lump sum of money
          The probability of having automobile insurance is 62.5%. The probability of having life insurance is 37.5%. The probability of having homeowners insurance is 50%. What is the probability of people who picked life insurance and homeowners insurance?

          Because there are only two there is no intersection of all 3. So I drew a venn diagram and labeled the intersections

          X = auto/life
          Y = auto/home
          Z = life/home

          Then

          X = .625 - Y
          X = .375 - Z
          Z = .50 - Y

          .375 - x = .50 - y ... x = y - .125

          x = y - .125
          + x = .625 - y

          ...2x = .50
          x=.25
          y=.375
          z=.125 (life and home)

          Comment

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