a bag contains 1 red, 1 yellow, 1 blue, and 1 green marble. what is the probability of choosing a green…

a bag contains 1 red, 1 yellow, 1 blue, and 1 green marble. what is the probability of choosing a green marble, not replacing it, and then choosing a red marble?\n\\(\\frac{1}{16}\\)\n\\(\\frac{1}{12}\\)\n\\(\\frac{1}{4}\\)\n\\(\\frac{1}{2}\\)

a bag contains 1 red, 1 yellow, 1 blue, and 1 green marble. what is the probability of choosing a green marble, not replacing it, and then choosing a red marble?\n\\(\\frac{1}{16}\\)\n\\(\\frac{1}{12}\\)\n\\(\\frac{1}{4}\\)\n\\(\\frac{1}{2}\\)

Answer

Explanation:

Step1: Calculate probability of choosing green marble

There are 4 marbles in total and 1 green marble. So the probability of choosing a green marble first is $\frac{1}{4}$.

Step2: Calculate probability of choosing red marble after green

After choosing a green marble and not - replacing it, there are 3 marbles left. The probability of choosing a red marble now is $\frac{1}{3}$.

Step3: Calculate combined probability

For two independent - like (in the non - replacement sense) events, we multiply the probabilities. So the probability of choosing a green marble first and then a red marble is $\frac{1}{4}\times\frac{1}{3}=\frac{1}{12}$.

Answer:

B. $\frac{1}{12}$