A roulette wheel has 38 slots, of which 18 are red, 18 black, and 2 green. A gambler will play three times, each time betting $5 on red. The gamblergets$10ifredoccursandlosesthe bet otherwise. Let X denote the net gain of the gambler in 3 plays ( for instance, if he loses all three times, then X-15 ).

(a)Obtain the probability distribution of X.

(b)Calculate the expected value of X.

(c)Will the expected net gain be different if the gambler alternates his bets between red and black? Why or why not?