Question

question 2
1 pts
suppose there are 12 marbles in a bag--3 blue, 5 red, 4 yellow. if two marbles are drawn from the bag without replacement between draws, what path along
the tree diagram is indicated from the draw of blue then blue, and what is the resulting probability?
first draw second draw
tree diagram omitted
options:
ad, 6/144
ad, 9/132
ad, 9/144
ad, 57/132
ad, 6/132
ad, 6/12

Explanation:

Step1: Probability of first blue

There are 3 blue marbles out of 12 total. So probability of first blue is $\frac{3}{12}$.

Step2: Probability of second blue (without replacement)

After drawing one blue, there are 2 blue left and 11 total. So probability is $\frac{2}{11}$.

Step3: Multiply the two probabilities

To find the probability of blue then blue, multiply the two probabilities: $\frac{3}{12} \times \frac{2}{11} = \frac{6}{132}$. The path is AD (first draw blue is A, second draw blue is D).

Answer:

AD, 6/132