In the game of billiards there are 9 colors of balls There i

In the game of billiards there are 9 colors of balls. There is a single solid white (cue) ball and a single solid black (8) ball. The remaining seven colors are red, orange, green, yellow, blue, purple, and brown. Within each of these colors one of the balls is striped and the other is solid. Consider an experiment where all 16 billiards balls are placed inside a box and then one is randomly picked out. Define the following events:

Event A: A purple ball is chosen
Event B: We choose a striped ball
Event C: We choose the black ball

Note: for the questions requiring a numeric probability you can enter your answer as in fraction form \'n/d\' or you can evaluate the fraction and enter as a decimal value. When entering a decimal value be sure to use 3 digit precision

A) P(purple) =  
B) P(striped) =  
C) The probability that the ball chosen at random is the black ball is:  
D) P(purple^c) =  
E) P(purple ? striped) =  
F) P(black ? striped) =  

Note: for parts G through J you only have 1 submission
G) True or False: We can conclude that the events purple and striped are independent  ---Select--- True False
H) True or False: We can conclude that the events purple and striped are mutually exclusive ---Select--- True False
I) True or False: We can conclude that the events black and striped are independent  ---Select--- True False
J) True or False: We can conclude that the events black and striped are mutually exclusive ---Select--- True False
K) The probability of selecting a purple ball given that the ball is striped is:  
L) (purple | striped^c) =  
M) The probability of selecting any colored ball other than purple given that the ball is striped is:

Solution

a) P(green) = 2 out of 16 = 2/16 = 1/8

b) P(solid) = 9 out of 16 = 9/16

c) P(black) = 1 out of 16 = 1/16

d) P(green)c = 1-P(green) = 1-1/8 = 7/8

e) P(green and solid) = 1 out of 16 = 1/16

f) P(black and solid) = 1 out of 16 = 1/16

g) False : because P(G&S) =1/16 not equal to P(G) * P(S) = 1/8 * 9/16

h) False : because P(G&S) = 1/16 which is not 0

i) False : P(B&S) = 1/16 not equal to P(B) * P(S) = 1/16 * 9/16

j) False : P(B&S) = 1/16 which is not 0 .

K) P(green|solid) = P(green and solid) / P(solid) = 1/9

L) P(green and not solid) = 1 out of 16 = 1/16

P(not solid ) = 1-P(solid) = 1-9/16 = 7/16

so P(green| not solid ) = P(green and not solid) / P(not solid) = 1/7

M) 1- P(green | solid) = 1-1/9 = 8/9