Question

(a) If the knowledge that an event A has occurred implies that a second event B cannot occur, then the events A and B are said to be A. collectively exhaustive. B. the sample space. C. mutually exclusive. D. independent. (b) If event A and event B are as above and event A has probability 0.2 and event B has probability 0.2, then the probability that A or B occurs is ____

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: 61 percent BLUE, 21 percent RED, and 18 percent GREEN.

(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

Part 1:

(a) Option: C. mutually exclusive (Since mutually exclusive means two events does not occur simultaneously).

(b) Since A and B are mutually exclusive then P(A and B)=0.

Given that P(A)=P(B)=0.2 then P(A or B)=P(A)+P(B)-P(A and B)=0.2+0.2-0=0.4.

Answer: 0.4.

Part 2:

(a) Let X=no. of times that the process is repeated until the pointer stops on BLUE

X follows geometric distribution with P(BLUE)=0.61.

P(X=3)=(1-P(BLUE))^2P(BLUE)=(1-0.61)^2*0.61= 0.0928.

(b) Let X=no. of times that the process is repeated until the pointer stops on RED

X follows geometric distribution with P(RED)=0.21.

(c) Let X=no. of times that the process is repeated until the pointer stops on GREEN

X follows geometric distribution with P(GREEN)=0.18.