GATE 2025 ES – Question 47
A family compares yearly pollution-related health costs. City1 has high exposure probability .1/cost10 lakh, mild .4/cost8 lakh, and low .5/cost4 lakh. City2 has high .2/cost8 lakh and low .8/cost1.5 lakh. Find expected City1 cost minus City2 cost, in lakh/year, to two decimals.
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Show answer and explanation
Correct answer: 3.20 to 3.60
Explanation
Expected cost weights each outcome by its probability. City1 gives $E_1=.1(10)+.4(8)+.5(4)=6.2$ lakh/year. City2 gives $E_2=.2(8)+.8(1.5)=2.8$ lakh/year. The difference is $6.2-2.8=\mathbf{3.40}$ lakh/year; the positive sign means City1 has the greater expected cost.