Question

A player throws a fair die and simultaneously flips a fair coin. If the coin lands heads, then she wins twice, and if tails, then she wins one-half of the value that appears on the die. Determine her expected winnings.

Answer 1

4.375

Step-by-step explanation:

Let random variable be X represent the result of toss coin

Let Y be the random variable represent number on dice.

Probability of getting heads = P(H) = 1/2

Probability of getting tails = P(T) = 1/2

Probability of getting number ob die

P(1) = P(2) = P(3) = P(4) = P(5) =P(6) = 1/6

Expected winning when coin landed head

`E_(Head)((Y)/(X)) = E(2Y).P(X = H)`

=
`2. (1)/(2)(1.(1)/(6)+2.(1)/(6)+3.(1)/(6).......+6..(1)/(6))`

= 3.5

Expected winning when coin landed tails

`E_(Tails)((Y)/(X)) = E((1)/(2)Y).P(X = T)`

=
`(1)/(2). (1)/(2)(1.(1)/(6)+2.(1)/(6)+3.(1)/(6).......+6..(1)/(6))`

= 0.875

Expected winning

=
`E_(Head)((Y)/(X)) + E_(Tails)((Y)/(X))`

= 3.5 + 0.875

= 4.375