Part One: Probability

A Color Sequence Experiment

Suppose that we have a special box - each time we press a button on the box, it prints out a sequence of colors, in order - it prints four colors at a time. Suppose the box follows the following Probabilities for each Color Sequence:

Color Sequence	Probability CS Prints Out
BBBB	.10 = 10%
BGGB	.25 = 25%
RGGR	.05 = 05%
YYYY	.30 = 30%
BYRG	.15 = 15%
RYYB	.15 = 15%
Total	1.00 = 100%

Let's define the experiment: We push the button, and then the box prints out exactly one(1) of the above listed color sequences. We then note the resulting(printed out) color sequence. Let's discuss the simple(or basic) events. The simple events are the color sequences. The probabilities for each color sequence are given in the table.

Suppose we define the event E={Blue(B) is printed in the 2^nd or 3^rd slot}. Compute the probability for event E, and show me how you did it. Also, interpret the probability for event E.

Suppose we define the event F={Yellow(Y) is printed at least once in the sequence}. Compute the probability for event F, and show me how you did it. Also, interpret the probability for event F.

Suppose we define the event G={Green(G) is printed in the 2^nd slot}. Compute the probability for event G, and show me how you did it. Also, interpret the probability for event G.

Suppose we define the event H={Red(R) is not the 1^st color}. Compute the probability for the event H, and use the Complementary Rule. Also, interpret the probability for H.

Suppose we define the event I={Blue(B) is not the 4^th color}. Compute the probability for the event I, and use the Complementary Rule. Also, interpret the probability for I.