Consider a play of the casino game 'Quick Draw'. In this game, the player pays

$10 to play. He/she picks one card from the standard deck of 52 cards (i.e. four A's, four K's,

etc.). If the player selects an "A", he/she wins $50; if the player selects a "K", he/she wins $30.

Otherwise, the player wins nothing. Let the random variable X represent the player's profit on a

single play of 'Quick Draw'.

a) Construct the probability distribution for the random variable X. [3]

b) What is the probability that the player makes money on a single play of the game? [1]

c) Calculate the expected value of the random variable X and provide an interpretation of its value

in the context of the question.