Part One: Probability

Case Study #1.11: Conditional Probability

Case Study Description: Compute conditional probabilities associated with the 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.

Compute Pr{ blue shows 1^st | blue shows 4^th };

Compute Pr{ green shows 2^nd or 3^rd | yellow shows };

Compute Pr{ yellow shows | red shows }.