Question

Hong rolls the cube once. He wins $1 if a 1 is rolled, $2 if a2 is rolled, $3if a3 is rolled, $4 is a 4 is rolled. He loses $6.50 if a 5 or 6 is rolled

Answer 1

a)

The expected value formula is

`E=\sum_ix_iP(x_i)`

Thus, in our case, after noticing that the probability of landing in a given number between 1 and 6 is equal to 1/6

`\begin{gathered} E=1((1)/(6))+2((1)/(6))+3((1)/(6))+4((1)/(6))-6.5((1)/(6)+(1)/(6)) \\ \Rightarrow E=(10)/(6)-(13)/(6) \\ \Rightarrow E=-(3)/(6)=-(1)/(2) \end{gathered}`

Thus, the answer to part a) is -0.5 dollars.

b)

An expected value of -0.5 dollars means that Hong can expect to lose 0.5 dollars per roll.