Question

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

\\(p(a \text{ and } d) = \frac{?}{\square}\\)

simplify your answer completely.

Explanation:

Identify the path probabilities

$$
LATEXBLOCK0
$$

Calculate the joint probability

$$ P(A \text{ and } D) = P(A) \times P(D \mid A) = \frac{2}{5} \times \frac{5}{6} = \frac{10}{30} $$

Simplify the fraction

$$ P(A \text{ and } D) = \frac{1}{3} $$

Answer:

The diagram below represents an experiment consisting of two independent trials. Find \(P(A \text{ and } D)\).

\(P(A \text{ and } D) =\) <blank>\(\frac{1}{3}\)</blank>

Simplify your answer completely.