Question

question 1
1 pts
suppose there are 12 marbles in a bag--3 blue, 5 red, 4 yellow. if two marbles are drawn from the bag with replacement between draws, what path along the
tree diagram is indicated from the draw of red then blue, and what is the resulting probability?
first draw second draw
options:
bg, 15/144
ae, 15/144
bg, 8/12
ae, 8/12
ae, 15/132
bg, 15/132

Explanation:

Step1: Determine the path

First, the first draw is Red, so we look at the branch for Red (labeled B). Then the second draw is Blue, so from the Red branch (B), the Blue sub - branch is G? Wait, no, looking at the tree: First draw branches: A (Blue), B (Red), C (Yellow). Then from B (Red), the second draw branches: G (Blue), H (Red), I (Yellow). So the path for first draw Red (B) and second draw Blue (G) is BG.

Step2: Calculate the probability of first draw Red

The total number of marbles is \(n = 12\), the number of red marbles is \(r=5\). The probability of drawing a red marble in the first draw (with replacement) is \(P(R)=\frac{5}{12}\).

Step3: Calculate the probability of second draw Blue

The number of blue marbles is \(b = 3\). Since we are drawing with replacement, the probability of drawing a blue marble in the second draw is \(P(B)=\frac{3}{12}\).

Step4: Calculate the combined probability

Since the two events (first draw Red and second draw Blue) are independent (because of replacement), the probability of both events happening is \(P = P(R)\times P(B)=\frac{5}{12}\times\frac{3}{12}=\frac{15}{144}\).

Answer:

BG, \( \frac{15}{144} \) (corresponding to the option BG, 15/144)