Aplayer 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.

4.375

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

=

= 3.5

Expected winning when coin landed tails

=

= 0.875

Expected winning

=

= 3.5 + 0.875

= 4.375