Question

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?
○ \\(\frac{1}{16}\\)
○ \\(\frac{1}{12}\\)
○ \\(\frac{1}{4}\\)
○ \\(\frac{1}{2}\\)

Explanation:

Step1: Probability of green marble

There are 4 marbles, 1 green. So \( P(\text{green}) = \frac{1}{4} \).

Step2: Probability of red after green

After removing green, 3 marbles left, 1 red. So \( P(\text{red}|\text{green}) = \frac{1}{3} \).

Step3: Multiply probabilities

For dependent events, \( P = \frac{1}{4} \times \frac{1}{3} = \frac{1}{12} \).

Answer:

\(\frac{1}{12}\) (corresponding to the option \(\boldsymbol{\frac{1}{12}}\))