a bag contains 9 green marbles, 3 red marbles, and 8 blue marbles. one marble is taken from the bag and put…

a bag contains 9 green marbles, 3 red marbles, and 8 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 green?\na $\frac{9}{50}$\nb $\frac{17}{20}$\nc $\frac{1}{19}$\nd $\frac{18}{95}$

a bag contains 9 green marbles, 3 red marbles, and 8 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 green?\na $\frac{9}{50}$\nb $\frac{17}{20}$\nc $\frac{1}{19}$\nd $\frac{18}{95}$

Answer

Answer:

A. $\frac{9}{50}$

Explanation:

Step1: Calculate total marbles

$9 + 3+8=20$

Step2: Probability of first - blue marble

The probability of getting a blue marble first is $P(\text{blue})=\frac{8}{20}$ since there are 8 blue marbles out of 20 total marbles.

Step3: Probability of second - green marble

Since the marble is replaced, the probability of getting a green marble second is $P(\text{green})=\frac{9}{20}$ as there are 9 green marbles out of 20 total marbles.

Step4: Calculate combined probability

Since the two events are independent, the probability that the first is blue and the second is green is $P = \frac{8}{20}\times\frac{9}{20}=\frac{72}{400}=\frac{9}{50}$.