Question

4. [6 marks] Consider a play of the casino game 'Quick Draw'. In this game, the player pays $10 to play. He/she picks onē 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 (i.e. the profit is $40); if the player selects a "K", he/she wins $30 (i.e. the profit is $20). Otherwise, the player wins nothing and also loses the bet of $10. 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 marks] b) What is the probability that the player makes money on a single play of the game? [1 mark] c) Calculate the expected value of the random variable X and provide an interpretation of its value in the context of the question. [2 marks]

Answer 1

X	p(X=x)
40	4/52
20	4/52
-10	44/52

here X represents profit of a player X= 40 when the player chooses A out of a deck of 52

X=20 when the player chooses K out of a deck of 52 cards.

X=-10 when the player chooses not A or not K

P(X=40)=4/52

P(X=20)=4/52

P(X=-10)=44/52