Question

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 then 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. p(gg) = 4/9 x = 1st pick 2nd pick 4/9 complete p(gy) = 2/9 x = 2/9 complete p(yg) = 2/9 complete p(yy) = done 12 of 12

Explanation:

Step1: Determine total number of marbles

There are 8 green marbles and 1 yellow marble, so total marbles = 8 + 1=9.

Step2: Calculate P(YY)

The probability of picking a yellow - marble on the first pick is $\frac{1}{9}$ since there is 1 yellow marble out of 9 total marbles. Since the marble is replaced, the probability of picking a yellow - marble on the second pick is also $\frac{1}{9}$.

Step3: Use the multiplication rule for independent events

For independent events A and B, P(A and B)=P(A)×P(B). Here, A is the event of picking a yellow marble on the first pick and B is the event of picking a yellow marble on the second pick. So P(YY)=$\frac{1}{9}\times\frac{1}{9}=\frac{1}{81}$.

Answer:

$\frac{1}{81}$