Question

the diagram below represents an experiment consisting of two independent trials. find p(b and c).

\\(p(b \text{ and } c) = \frac{?}{}\\)

simplify your answer completely.

Explanation:

Identify the path on the tree diagram

Using the Probability Tree Diagrams knowledge point

• First trial outcome: \(B\), with probability \(P(B) = \frac{3}{5}\)
• Second trial outcome: \(C\), with probability \(P(C|B) = \frac{1}{6}\)

Calculate the joint probability

Using the Independent Events Probability and Tree Diagram Multiplication knowledge points

$$ P(B\text{ and }C) = P(B) \times P(C|B) = \frac{3}{5} \times \frac{1}{6} = \frac{3}{30} = \frac{1}{10} $$

Answer:

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

\(P(B\text{ and }C) =\) <blank>\(\frac{1}{10}\)</blank>

Simplify your answer completely.