Question

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Explanation:

Identify the path for the event B and D

Using the Probability Tree Diagrams knowledge point
To find \(P(B\text{ and }D)\), we trace the path on the tree diagram that starts from the root, goes to node \(B\), and then goes to node \(D\).

Extract the branch probabilities

Using the Probability Tree Diagrams knowledge point

• The probability of choosing the branch to \(B\) from the start is \(P(B) = \frac{2}{3}\).
• The conditional probability of choosing the branch to \(D\) given that we are at \(B\) is \(P(D|B) = \frac{1}{4}\).

Calculate the joint probability

Using the Tree Diagram Multiplication and Independent Events Probability knowledge points

$$ P(B\text{ and }D) = P(B) \times P(D|B) = \frac{2}{3} \times \frac{1}{4} = \frac{2}{12} = \frac{1}{6} $$

Answer:

The diagram below represents an experiment consisting of two independent trials. Find P(B and D).

\(P(B\text{ and }D) =\) <blank>\(\frac{1}{6}\)</blank>

Simplify your answer completely.