To answer this question, we can proceed as follows:
1. Count the total of gummy worms into the bag:
12 green + 3 blue + 6 red + 2 orange = 23 gummy worms.
2. In the first event (pull a red worm), we have that the probability of it is:
[tex]P(R)=\frac{6}{23}[/tex]Since we have 6 red gummy worms from a total of 23.
3. Now, the probability of the second event is a little different. You have eaten one of the red gummy worms. Then, we have a total of 23 - 1 = 22 gummy worms.
The probability, now, of getting a green worm is (there are 12 green gummy worms):
[tex]P(G)=\frac{12}{22}\Rightarrow P(G)=\frac{6}{11}[/tex]4. Finally, the probability of these two events is, applying the multiplication rule:
[tex]P(R\cap G)=\frac{6}{23}\cdot\frac{6}{11}\Rightarrow P(R\cap G)=\frac{36}{253}[/tex]Then, the answer is 36/253 (second option.)
This is a case of conditional probability. We see that the probability of the second event was influenced by the first event.
