Question

In a carnival game, a player spins a wheel that stops with the pointer on one (and only one) of three colors. The likelihood of the pointer landing on each color is as follows: 62 percent BLUE, 24 percent RED, and 14 percent GREEN.

Note: Your answers should be rounded to three decimal places.

(a) Suppose we spin the wheel, observe the color that the pointer stops on, and repeat the process until the pointer stops on BLUE. What is the probability that we will spin the wheel exactly three times?

(b) Suppose we spin the wheel, observe the color that the pointer stops on, and repeat the process until the pointer stops on RED. What is the probability that we will spin the wheel at least three times?

(c) Suppose we spin the wheel, observe the color that the pointer stops on, and repeat the process until the pointer stops on GREEN. What is the probability that we will spin the wheel 2 or fewer times?

Answer 1

Given:

P(BLUE) = 0.62

P(RED) = 0.24

P(GREEN) = 0.14

When we are interested in the random variable, X such that the number of trials until the first success occurs, the random variable follows a geometric distribution.

a)

Let the random variable, X = number of trials until. the pointer stops on BLUE

The random variable X follows a geometric distribution with probability mass function,

b)

Let the random variable, X = number of trials until. the pointer stops on RED

The random variable X follows a geometric distribution with the following cumulative distribution function,

c)

Let the random variable, X = number of trials until. the pointer stops on GREEN

The random variable X follows a geometric distribution with the following cumulative distribution function,