carmen had 8 green marbles, 6 red marbles, and 2 yellow marbles in a bag. she pulled a marble from the bag…

carmen had 8 green marbles, 6 red marbles, and 2 yellow marbles in a bag. she pulled a marble from the bag at random and then put it back. then she asked her brother to pull a marble from the bag at random. what is the probability that carmen chose a green marble and her brother chose a red one? write your answer as a fraction or decimal. do not round.

carmen had 8 green marbles, 6 red marbles, and 2 yellow marbles in a bag. she pulled a marble from the bag at random and then put it back. then she asked her brother to pull a marble from the bag at random. what is the probability that carmen chose a green marble and her brother chose a red one? write your answer as a fraction or decimal. do not round.

Answer

Explanation:

Step1: Calculate total number of marbles

$8 + 6+2=16$

Step2: Calculate probability of Carmen choosing green marble

The probability of Carmen choosing a green marble is $\frac{8}{16}$ since there are 8 green marbles out of 16 total marbles.

Step3: Calculate probability of brother choosing red marble

The probability of her brother choosing a red marble is $\frac{6}{16}$ since there are 6 red marbles out of 16 total marbles.

Step4: Calculate joint - probability

Since the two events are independent (because the marble is put back), the joint - probability is the product of the two probabilities. So $P=\frac{8}{16}\times\frac{6}{16}=\frac{48}{256}=\frac{3}{16}= 0.1875$

Answer:

$\frac{3}{16}$ or $0.1875$