Question

Consider a roulette wheel, where we are referring to the gambling wheel featured in casinos or gambling parlors around the world. It is a wheel that has two green slots (the 0, and 00 slots on an American table; recall, American wheels are different than European wheels), 18 red slots, and 18 black slots. i) What is the probability it will take x = 1 trial or spin of the wheel before observing r = 1 green slot?

Answer 1

The probability of observing 1 green slot in 1 trial of the roulette wheel is 2/38. The probability of observing 1 green slot in x trials can be calculated as (36/38)^(x-1) * (2/38).

Step-by-step explanation:

To find the probability that it will take 1 trial or spin of the roulette wheel before observing 1 green slot, we need to consider the total number of possible outcomes and the number of favorable outcomes.

There are 2 green slots and a total of 38 slots on the roulette wheel (2 green + 18 red + 18 black). So, the probability of observing 1 green slot in 1 trial is 2/38.

The probability of observing 1 green slot in x trials is the probability of not observing a green slot in (x-1) trials multiplied by the probability of observing a green slot in the xth trial. This can be represented as (36/38)^(x-1) * (2/38).

For example, the probability of observing 1 green slot in the first trial is (36/38)^0 * (2/38) = 2/38 = 1/19.