the drawing below shows the different colors of marbles in a bag. marco will randomly choose marbles from…

the drawing below shows the different colors of marbles in a bag. marco will randomly choose marbles from the bag. what is the probability of the following outcomes? 12. marco chooses a red marble, replaces it, then chooses a white marble = ______ 13. marco chooses a white marble, does not replace it, then chooses a blue marble = ______ 14. marco chooses a blue marble, does not replace it, then chooses a red marble = ______ 15. marco chooses a blue marble, replaces it, then chooses another blue marble = ______

the drawing below shows the different colors of marbles in a bag. marco will randomly choose marbles from the bag. what is the probability of the following outcomes? 12. marco chooses a red marble, replaces it, then chooses a white marble = ______ 13. marco chooses a white marble, does not replace it, then chooses a blue marble = ______ 14. marco chooses a blue marble, does not replace it, then chooses a red marble = ______ 15. marco chooses a blue marble, replaces it, then chooses another blue marble = ______

Answer

Explanation:

Step1: Count total marbles

There are 8 marbles in total (4 red, 2 white, 2 blue).

Step2: Calculate probability for 12

The probability of choosing a red marble first is $\frac{4}{8}$ since there are 4 red marbles out of 8. Since it's replaced, the probability of choosing a white marble next is $\frac{2}{8}$. The combined - probability is $\frac{4}{8}\times\frac{2}{8}=\frac{8}{64}=\frac{1}{8}$.

Step3: Calculate probability for 13

The probability of choosing a white marble first is $\frac{2}{8}$. Without replacement, there are 7 marbles left. The probability of choosing a blue marble next is $\frac{2}{7}$. The combined - probability is $\frac{2}{8}\times\frac{2}{7}=\frac{4}{56}=\frac{1}{14}$.

Step4: Calculate probability for 14

The probability of choosing a blue marble first is $\frac{2}{8}$. Without replacement, there are 7 marbles left. The probability of choosing a red marble next is $\frac{4}{7}$. The combined - probability is $\frac{2}{8}\times\frac{4}{7}=\frac{8}{56}=\frac{1}{7}$.

Step5: Calculate probability for 15

The probability of choosing a blue marble first is $\frac{2}{8}$. Since it's replaced, the probability of choosing a blue marble next is also $\frac{2}{8}$. The combined - probability is $\frac{2}{8}\times\frac{2}{8}=\frac{4}{64}=\frac{1}{16}$.

Answer:

  1. $\frac{1}{8}$
  2. $\frac{1}{14}$
  3. $\frac{1}{7}$
  4. $\frac{1}{16}$