The game of roulette uses a wheel containing 38 pockets Thir

The game of roulette uses a wheel containing 38 pockets. Thirty six pockets are numbered 1, 2, ..., 36, and the remaining two are marked 0 and 00. The wheel is spun and a pocket is identified as the winner. Assume that the observance of any one pocket is just as likely as any other.

a) What is the probability that the winning number is odd? (assuming that 0 and 00 are neither even or odd)

b) Let A be the event that any odd number is the winning number. Let B be the even that any number between 1 and 20 is the winning number. What is the intersection between events A and B equal to?

Solution

a) P(odd) = P(1,3,5...,37) = 18/38 = 0.47368

b) Intersection is event that number is odd and between 1 and 20, i.e, number is in set (1,3,5,7,9,11,13,15,17,19)