derek and mia place two green marbles and one yellow marble in a bag. somebody picks a marble out of the bag…

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

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

Answer

Answer:

$\frac{4}{9}$

Explanation:

Step1: Calculate probability of first - green pick

There are 2 green marbles and 1 yellow marble, so total 3 marbles. Probability of picking a green marble on the first pick, $P(G_1)=\frac{2}{3}$.

Step2: Calculate probability of second - green pick

Since the marble is replaced, again there are 3 marbles. Probability of picking a green marble on the second pick, $P(G_2)=\frac{2}{3}$.

Step3: Calculate probability of two - green picks

By the multiplication rule for independent events $P(GG)=P(G_1)\times P(G_2)=\frac{2}{3}\times\frac{2}{3}=\frac{4}{9}$.