Subjects probability

Hail Prediction 40D3Ac

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1. **State the problem:** We want to find the fraction of days when it actually hailed and Leon's prediction was correct. 2. **Identify relevant data:** From the frequency tree: - Total days = 53 - Days predicted hail = 27 - Days predicted no hail = 26 - Days it actually hailed and predicted hail = 14 - Days it actually hailed and predicted no hail = 21 3. **Understand the question:** We want the fraction of days when it hailed that Leon predicted hail correctly. 4. **Calculate total days it hailed:** $$\text{Total hail days} = 14 + 21 = 35$$ 5. **Calculate fraction of correct hail predictions:** $$\text{Fraction} = \frac{\text{Days predicted hail and actually hailed}}{\text{Total hail days}} = \frac{14}{35}$$ 6. **Simplify the fraction:** $$\frac{14}{35} = \frac{2}{5}$$ **Final answer:** The fraction of days when it hailed and Leon's prediction was correct is $\frac{2}{5}$.