In a carnival game a player spins a wheel that stops with th

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: 65 percent BLUE, 21 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?

Solution

b) the probability that we will spin the wheel at least three times = Prob first two spins non blue and third blue

= (0.21+0.14)(0.65)

= 0.2275

c) probability that we will spin the wheel 2 or fewer times

= Prob for first spin green or prob for first non green and second green

= 0.14+(0.86)0.14

=0.2604