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Random Variables, Expectation & Variance · Question 49 of 68

What premium would make the insurer's expected gain on the policy exactly zero?

Question 49

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 premium would make the insurer's expected gain on the policy exactly zero?

Options for question 49

Show the answer and explanation
CorrectNot quiteAnswer A

Correct answer: A

Explanation

  1. With premium PP, the expected gain is P−0.005×1,00,000=P−500P - 0.005 \times 1{,}00{,}000 = P - 500.

  2. Zero when P=500P = 500 rupees, the fair premium.

Worth noting

₹1,500 is the expected gain at the ₹2,000 premium, not a premium.

Concept
A fair price has zero expected gain
Typical time
120 s
Your time
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The rule this testsMathematical expectation
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