Suppose you want to play a carnival game that costs 4 dollars each time you play. If you win, you get $100. The probability of winning is 1⁄100. What is the expected value of the amount the carnival stands to gain?

The answer is: -3

Step-by-step explanation:

The expected value is given by adding the values of posible gain mutiplied by the probability of getting that gain so you lose the $4 you pay to play the game with probability 1-1/100=99/100 and you gain 100-4=96 dollars if you win with probability 1/100, so

geometry: triangles

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call the larger triangle abc

then the smaller triangle cde is similar to abc (all angles are equal, aaa).  

ab is the side that is 36, and we wish to find de, the side corresponding to ab

area_cde = area_abc - area_cde --> area_abc / area_cde = 2

let x=length of de

ratio of areas = (ratio of sides)^2

+2+=+%2836%2fx%29%5e2+

+2+=+1296%2fx%5e2+

++x%5e2+=+1296%2f2+=+648+

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