Question

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

Explanation:

Step1: Recall probability - multiplication rule for independent events

For two independent events, the probability of both occurring is the product of their individual probabilities.

Step2: Identify probabilities of A and D

The probability of event A is $P(A)=\frac{1}{4}$, and the probability of event D given A is $P(D|A)=\frac{5}{8}$. Since the trials are independent, $P(A\cap D)=P(A)\times P(D|A)$.

Step3: Calculate the probability

$P(A\cap D)=\frac{1}{4}\times\frac{5}{8}=\frac{5}{32}$

Answer:

$\frac{5}{32}$