1. Diberikan probabilitas: - $P(A) = 0.25$ - $P(B \mid A^c) = 0.87$ - $P(A \cap B) = 0.20$ Kita diminta mencari $P(B)$ dan $P(A \mid B)$. 2. Rumus yang digunakan: - Probabilitas komplemen: $P(A^c) = 1 - P(A)$ - Probabilitas total untuk $B$: $$P(B) = P(B \cap A) + P(B \cap A^c) = P(A \cap B) + P(B \mid A^c) \times P(A^c)$$ - Probabilitas kondisional: $$P(A \mid B) = \frac{P(A \cap B)}{P(B)}$$ 3. Hitung $P(A^c)$: $$P(A^c) = 1 - 0.25 = 0.75$$ 4. Hitung $P(B)$: $$P(B) = 0.20 + 0.87 \times 0.75 = 0.20 + 0.6525 = 0.8525$$ 5. Hitung $P(A \mid B)$: $$P(A \mid B) = \frac{0.20}{0.8525} \approx 0.2347$$ --- 6. Diberikan probabilitas baru: - $P(A) = 0.7$ - $P(B) = 0.6$ - $P(A \cap B) = 0.35$ Diminta mencari $P(B)$ dan $P(A \mid B)$ (meskipun $P(B)$ sudah diketahui). 7. Hitung $P(A \mid B)$: $$P(A \mid B) = \frac{P(A \cap B)}{P(B)} = \frac{0.35}{0.6} \approx 0.5833$$ Jawaban akhir: - $P(B) = 0.8525$ - $P(A \mid B) \approx 0.2347$ - $P(B)$ (diberikan) = 0.6 - $P(A \mid B) \approx 0.5833$