1. **State the problem:** Jake has three guitar picks: green (G), yellow (Y), and black (B). He randomly selects one pick before each concert. We want to find the probability that he selects the same color pick for two concerts in a row.
2. **Understand the sample space:** For two concerts, each pick can be any of the three colors. So, the total number of possible outcomes is $3 \times 3 = 9$.
3. **Identify favorable outcomes:** The favorable outcomes are when the first and second picks are the same color. These are: GG, YY, BB.
4. **Calculate the probability:**
$$\text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{3}{9}$$
5. **Simplify the fraction:**
$$\frac{3}{9} = \frac{\cancel{3} \times 1}{\cancel{3} \times 3} = \frac{1}{3}$$
6. **Final answer:** The probability that Jake selects the same color pick for two concerts in a row is **$\frac{1}{3}$**.
Probability Same Pick 795Cc7
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