A roulette wheel has 38 pockets numbered 1 through 36 as well as two pockets lab

Question

A roulette wheel has 38 pockets numbered 1 through 36 as well as two pockets labeled '0' and '00'. There are 18 red pockets, 18 black pockets, and 2 green pockets ('0' and '00'). To play roulette, a metal ball is spun around the wheel and lands inside one of the pockets. a. What is the probability that the ball does not land in a red pocket? b. What is the probability that the ball lands in a pocket that contains the digit '2'? c. Suppose the ball is spun twice. What is the probability that the ball lands in a black pocket both times? Assume the spins are independent from one another. d. Suppose the ball is spun twice. What is the probability that the ball lands in a black pocket on at least one of the two spins? Assume the spins are independent from one another.

Explanation / Answer

a) as there are 20 pocket except red out of 38

hence probability=20/38=10/19

b)as there are 13 pocket (2,12,20-29,32) that contains digit 2, hence probability =13/38

c)probabilty that it will land in black pocket both times=(18/38)*(18/38)=81/361

d)probabilty =1-P(ball does not land in black pocket even in single attempt)=1-(20/38)*(20/38)=261/361

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