Question

You will note the wheel has 38 slots. There are two green slots (labeled

0,00) and 36 slots which alternate red/black and are numbered 01-36. A
player participates by tossing a small ball around the wheel as the wheel
spins, and the ball lands in one of the 38 slots. The goal is for the ball to
land in a slot that the player predicted it would, and bet money on
happening. Define the following events:
E = The ball lands in an even numbered slot
M = The ball lands in a slot that is numbered a multiple of three (3,6,9,
12, etc...)
Use the given information to calculate the conditional probability M|E.
Round your answer to four decimal places.

Answer 1

~0.3158

Explanation:

Number of even numbers in the range of 1 - 38 is 38/2 = 19

=> P(E) = 19/38 = 1/2

Having: 38 = 3 x 12 + 2, then the number of numbers that is a multiple of 3 in the range of 1 - 38 is 12

=> P(M) = 12/38 = 6/19

Having: 38 = 6 x 6 + 2, then the number of numbers that is a multiple of 6 (or multiple of 2 and 3) is 6

=> P(E and M) = 6/38 = 3/19

Applying the conditional probability formula:

P(M|E) = P(E and M)/P(E) = (3/19)/(1/2) = 6/19 = ~0.3158