Question

What if I had an unfair coin flip game where a head had a likelihood of one in a million bu realization of $1,000,000 while a tail would mean $100,000 with the appropriate probability when the coin can only be one of two realizations. Find the expected value of this game and contrast your result with calculations associated with uninformed weights on the realizations What is the point?

Answer 1

Answer-

The probability of head has an amount of $ 1000000 is = 1 / 1 million = 1 / 1000000 = 0.000001
The probability of tail has an amount of $ 100000 is = 1 - ( 1 /1 million) = 1 - 0.000001 = 0.999999

Expected value of the game = Amount of head x probability of head + Amount of tail x probability of tail
Expected value of the game = $ 1000000 x 0.000001 + $ 100000 x 0.999999
= $ 1.0 + $ 99999.9
= $ 100000.9

In contrast the result of flip of a coin has a 50:50 probability of head and tail

Therefore
Expected value of the game = $ 1000000 x 0.5 + $ 100000 x 0.5
= $ 500000 + $ 50000
​​​​​​​= $ 550000