Question

Yuto has a bag containing 3 red marbles, 5 blue marbles, 2 green marbles, and 8 yellow marbles. Rin reaches into the bag, pulls out a blue marble, and puts it in her pocket. Then Misaki reaches in and pulls out a marble. What is the total number of possible outcomes for Misaki’s marble?
13
14
17
18

Answer 1

To determine the total number of possible outcomes for Misaki's marble after Rin pulls out a blue marble, we can start by calculating the total number of marbles currently in the bag before any marble is removed.

Initially, Yuto's bag contains:
- Red marbles: 3
- Blue marbles: 5
- Green marbles: 2
- Yellow marbles: 8

Calculating the total number of marbles:
\[
3 \, (\text{red}) + 5 \, (\text{blue}) + 2 \, (\text{green}) + 8 \, (\text{yellow}) = 18 \, \text{marbles}
\]

After Rin pulls out one blue marble, the number of each type of marble remaining in the bag is as follows:
- Red marbles: 3 (unchanged)
- Blue marbles: 5 - 1 = 4
- Green marbles: 2 (unchanged)
- Yellow marbles: 8 (unchanged)

Now calculate the new total number of marbles in the bag after Rin's action:
\[
3 \, (\text{red}) + 4 \, (\text{blue}) + 2 \, (\text{green}) + 8 \, (\text{yellow}) = 17 \, \text{marbles}
\]

Thus, there are 17 possible outcomes (types of marbles) for Misaki's marble.

The answer is \(\boxed{17}\).