Subjects probability

Train Track Probability 170907

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1. **State the problem:** Carly has picked some pieces of train track: 8 straight, 7 curved, 4 cross, and 5 switch tracks. We want to find the probability that the next piece she picks is straight. 2. **Recall the probability formula:** Probability of an event = \( \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}} \). 3. **Identify favorable outcomes:** The favorable outcomes are picking a straight track, which is 8 pieces. 4. **Calculate total pieces picked so far:** \(8 + 7 + 4 + 5 = 24\). 5. **Calculate the probability:** $$ \text{Probability} = \frac{8}{24} $$ 6. **Simplify the fraction:** $$ \frac{8}{24} = \frac{\cancel{8}^1}{\cancel{24}^3} = \frac{1}{3} $$ 7. **Interpretation:** The probability that the next piece Carly picks is straight is \(\frac{1}{3}\).