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Random Variables, Expectation & Variance · Question 47 of 68

What is the insurer's expected gain on one policy?

Question 47

MediumOriginal question

An insurer sells a one-year policy for a premium of ₹2,000. If the holder has an accident in the year, which happens with probability 0.005, the insurer pays out ₹1,00,000.

What is the insurer's expected gain on one policy?

Options for question 47

Show the answer and explanation
CorrectNot quiteAnswer C

Correct answer: C

Explanation

  1. The insurer keeps ₹2,000 with probability 0.995 and loses 1,00,000−2,000=98,0001{,}00{,}000 - 2{,}000 = 98{,}000 with probability 0.005.

  2. 2,000(0.995)−98,000(0.005)=1,990−490=1,5002{,}000(0.995) - 98{,}000(0.005) = 1{,}990 - 490 = 1{,}500 rupees.

Worth noting

₹1,490 forgets the premium is kept in the accident year too, taking off the full ₹1,00,000.

Concept
Expected gain with two outcomes
Typical time
120 s
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Ten questions from Random Variables, Expectation & Variance, at your own pace.

Practise this chapter →

Ten questions from Random Variables, Expectation & Variance, at your own pace.