Derek and mia place two green marbles and one yellow marble in a bag. somebody picks a marble out of the bag without looking and records its color (g for green and y for yellow). they replace the marble and then pick another marble. if the two marbles picked have the same color, derek loses 1 point and mia gains 1 point. if they are different colors, mia loses 1 point and derek gains 1 point. what is the expected value of the points for derek and mia?
ask for details follow report by paynedaisa 08/04/2017

Step-by-step explanation:

With each draw, the probability of selecting a green marble is 2/3 and the probability of selecting a yellow marble is 1/3.

To pick two of the the same color, they can either pick green twice or yellow twice.  

P = (2/3)(2/3) + (1/3)(1/3)

P = 5/9

To pick two different colors, they can either pick green first then yellow, or yellow first then green.

P = (2/3)(1/3) + (1/3)(2/3)

P = 4/9

Expected value for Derek is:

D = (5/9)(-1) + (4/9)(1)

D = -1/9

The expected value for Mia is:

M = (5/9)(1) + (4/9)(-1)

M = 1/9

351.23

step-by-step explanation: