Question

a bag contains 4 green marbles, 3 red marbles, and 7 blue marbles. one marble is taken from the bag and put back after checking its color. a second marble is then taken out. what is the probability that the first is blue and the second red?

Explanation:

Step1: Calculate total marbles

Total marbles = 4 + 3+ 7=14

Step2: Calculate probability of first - blue

Probability of first marble being blue, $P(\text{blue}_1)=\frac{7}{14}=\frac{1}{2}$

Step3: Calculate probability of second - red

Since the first marble is put back, total marbles remain 14. Probability of second marble being red, $P(\text{red}_2)=\frac{3}{14}$

Step4: Calculate joint probability

Since the two events are independent (because of replacement), the probability that the first is blue and the second is red is $P = P(\text{blue}_1)\times P(\text{red}_2)=\frac{1}{2}\times\frac{3}{14}=\frac{3}{28}$

Answer:

D. $\frac{3}{28}$