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.

What is the probability that the winning number is between 1 and 12 given that the winning number is even?

Solution

P(1 to 12 given it is even) = number of ways it can be even and in range (1,12) / (total number of ways it can be even)

= 6/19 = 0.3158 (Assuming 0 as even and 00 not even)

or = 6/20 = 0.3 (assuming both 0 and 00 are even)

or = 6/18 = 0.3333 (assuming neither 0 nor 00 even)