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 probability of event M. Round your answer to four decimal places.

P(M) = 0.3158

Step-by-step explanation:

Data given in the question:

Total Slots = 38

Green Slots = 2 labelled (0, 00)

Red Slots = 18

Black Slots = 18

E = Ball lands on an even numbered slot

M = Ball lands in a slot that is numbered a multiple of 3

We are required to find the probability of event M. For that, we need to identify how many multiples of 3 are present on the wheel.

Multiples of 3 between 1-36 = 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36

There are a total of 12 slots numbered with multiples of 3.

P(M) = No. of slots numbered a multiple of 3 / Total no. of slots

       = 12/38

P(M) = 0.3158 (rounded to four decimal places).

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