Two dice are rolled and two fair coins are tossed. Let X be the sum of the number of spots that show on the top faces of the dice and the number of coins that land heads up. The expected value of X is _____ .

Answer 1

Well, the die are independent.

expected dots from one die:1/6(1+2+3+4+5+6)=21/6
expected sum:= 42/6=7

expected number of heads: 1/2 * 2

expected value of X is 8

Answer 2

A lottery offers one $900 prize, one $600 prize, three $400 prizes, and five $100 prizes. One thousand tickets are sold at $6 each. Find the expectation of a person buys five tickets.