let x= the outcome when a fair die is rolled once. note that the expected value

Question

let x= the outcome when a fair die is rolled once. note that the expected value to be rolled is 3.5. before the die is rolled, you have two options:

take $ 2 upfront ( this is 7/3.5) or you can gamble and get $ 7divided by the value rolled (this is 7/x).

(a) name the smallest amount of money you might win by gambling or the smallest possible value of 7/x.

(b)what is the probability you would win this smallest amount by gambling

(c) would you expect to get more by gambling? find E[7/x] and see how this compares to $ 2

Explanation / Answer

A) THE HIGHEST VALUE A DICE CAN TAKE = 6

THEREFORE THE SMALLEST OR MINIMUM VALUE WHICH TO BE WON WILL BE 7/6 = $1.16

B) THE PROBABILITY OF HAVING 6 IN A DICE = 1/6

ALSO HERE IN THE GAME WE HAVE EQUAL CHANCES OF PLAYING 7/3,5 OR 7/X

SO THE PROBABILITY OF WINNING THE SMALLEST AMOUNT = 0.5*1/6 = 0.083

C) E(7/X) = 7/1*(1/6) + 7/2*(1/6)+7/3*(1/6)+7/4*(1/6)+7/5*(1/6)+7/6*(1/6) = 2.858

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