Question: Compute the indicated probabilities by referring to the probability tree. (A) P(MnS) (B) P(R) 0.3…

Compute the indicated probabilities by referring to the probability tree. (A) P(MnS) (B) P(R) 0.3 0.7 R M S 0.3 0.1 R N 0.7 0.9 S … (A) P(MnS) = 0.09 (Type an integer or a decimal.) (B) P(R) = (Type an integer or a decimal.)

Solution

To find \( P(R) \), we need to consider both paths that end with \( R \) in the probability tree: 1. Path \( M \to R \) 2. Path \( N \to R \) Calculate the probability for each path and then sum them up: Start with Path \( M \to R \): \[ P(M) = 0.3 \] \[ P(R \mid M) = 0.7 \] \[ P(M \cap R) = P(M) \cdot P(R \mid M) = 0.3 \cdot 0.7 = 0.21 \] Now, for Path \( N \to R \): \[ P(N) = 0.7 \