Problem

Complete the tree with first branches \(A=0.30\) and not \(A=0.70\), then place the two different conditional \(B\) rates on their matching second branches. Compute the \(A\text{-}\text{then}\text{-}B\) path.

Prompt probability tree: P(A)=0.30, P(B given A)=0.50, and P(B given not A)=0.20. Complementary branches and the A-then-B product are unknown.

Big Picture

What this problem is really about

A probability tree must attach each second-stage rate to the branch that supplies its condition. We’ll complete every complementary split to one, keep the two B rates on their matching first branches, trace the named A-then-B route, and multiply only the probabilities along that path.

Answer choices

Choose your path.

Preview only

The tree begins with A (0.30) or not A (0.70). After A, B is 0.50; after not A, B is 0.20. The A-then-B path has probability 0.30 × 0.50 = 0.15.

After both A and not A, the tree uses B = 0.20, so the A-then-B path is 0.30 × 0.20 = 0.06.

The same unconditional second-stage probability is used after A and after not A, so no joint probability is calculated.

The tree uses the stated branches, but P(A and B) is found by adding 0.30 and 0.50 to get 0.80.

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Complete the tree with first branches \(A=0.30\) and not \(A=0.70\), then place the two different conditional \(B\) rates on their matching second branches. Compute the \(A\text{-}\text{then}\text{-}B\) path.

What this problem is really about

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