1. The problem asks to find the probability $P(B)$ using the tree diagram. 2. According to the problem, $P(B) = P(M \cap B) + P(N \cap B)$. 3. From the tree diagram: - $P(M) = 0.7$, $P(N) = 0.3$. - Given $M$, $P(B|M) = 0.4$. - Given $N$, $P(B|N) = 0.5$. 4. Use the multiplication rule for joint probabilities: $$P(M \cap B) = P(M) \times P(B|M) = 0.7 \times 0.4 = 0.28$$ $$P(N \cap B) = P(N) \times P(B|N) = 0.3 \times 0.5 = 0.15$$ 5. Add these to find $P(B)$: $$P(B) = 0.28 + 0.15 = 0.43$$ 6. Therefore, the probability $P(B)$ is 0.43.