SOLUTION: A tree diagram has two stages. Stage 1 has two nodes and stage 2 has four nodes. In stage 1, the branch from the starting position to node A is labeled 0.3. The branch from the st

Algebra ->  Probability-and-statistics -> SOLUTION: A tree diagram has two stages. Stage 1 has two nodes and stage 2 has four nodes. In stage 1, the branch from the starting position to node A is labeled 0.3. The branch from the st      Log On


   



Question 1196656: A tree diagram has two stages. Stage 1 has two nodes and stage 2 has four nodes.
In stage 1, the branch from the starting position to node A is labeled 0.3. The branch from the starting position to node B is an answer blank.
In stage 2, the branch from node A to node C is an answer blank. The branch from node A to node D is labeled 0.4.
In stage 2, the branch from node B to node C is labeled 0.2. The branch from node B to node D is an answer blank.
Outcome
P(A ∩ C) =
P(A ∩ D) =
P(B ∩ C) =
P(B ∩ D) =

Answer by MathLover1(20850) About Me  (Show Source):
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given:
Stage 1 has two nodes and stage 2 has four nodes.
In stage 1, the branch from the starting position to node A is labeled 0.3. The branch from the starting position to node B is an answer blank.
In stage 2, the branch from node A to node C is an answer blank. The branch from node A to node+D is labeled+0.4.
In stage 2, the branch from node B to node C is labeled+0.2. The branch from node B+to node+D+is an answer blank.

recall: The sum of the probabilities on the branches leaving any node is always 1. This allows us to fill in the middle two blanks.

then
In stage 1, the branch from the starting position to node A is labeled 0.3. The branch from the starting position to node B+ will be 0.7.
In stage 2, the branch from node A to node+C is+0.6. The branch from node A to node D will be labeled 0.4.
In stage 2, the branch from node B+to node C is labeled 0.2. The branch from node B to node D will be+0.8.


Outcome
P(A ∩ C) =0.3%2A0.6=0.18
P(A ∩ D) =0.3%2A0.4=0.12
P(B ∩ C) =0.7%2A0.2=0.14
P(B ∩ D) =0.7%2A0.8=0.56