A state has a lottery game where a person picks one of the 1000 three-digit numbers between 000 and 999. The lottery selects a three-digit number at random. With a bet of $1, a person wins $600 if their number is selected and nothing ($0) otherwise. Complete parts a through d below. a. With a single $1 bet, what is the probability of winning $600? 0.001 (Do not round.) b. Let X denote the winnings for a $1 bet, so x = $0 or x =$600. Construct the probability distribution for X. X P(x) 0.999 $600 0.001 (Do not round.) c. Show that the mean of the distribution equals 0.60, corresponding to an expected return of 60 cents for the dollar paid to play. Choose the correct answer below. O A. 0+P(0) + 600 + P(600) = 0.60 OB. O . P(0) + 600 . P(600) = 0.60 O C. 0 . P(0) . 600 . P(600) = 0.60 OD. 0+ P(0) . 600 + P(600) = 0.60