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?

Explanation:

Step1: Calculate the probability of choosing a green marble first

The total number of marbles is \(1 + 1+1 + 1=4\). The probability of choosing a green marble \(P(G)=\frac{1}{4}\).

Step2: Calculate the probability of choosing a red marble second (without replacement)

After choosing a green marble, there are \(4 - 1=3\) marbles left. The probability of choosing a red marble \(P(R)=\frac{1}{3}\).

Step3: Use the multiplication rule for dependent events

The multiplication rule for dependent events is \(P(A\cap B)=P(A)\times P(B|A)\). Here \(A\) is choosing a green marble and \(B\) is choosing a red marble. So \(P(G\cap R)=\frac{1}{4}\times\frac{1}{3}=\frac{1}{12}\).

Answer:

\(\frac{1}{12}\)