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

Answer:

$\frac{2}{21}$

Explanation:

Step1: Recall probability - multiplication rule for independent events

For two independent events, $P(A\cap C)=P(A)\times P(C|A)$. Since the trials are independent, $P(C|A) = P(C)$.

Step2: Identify the probability of event A

From the tree - diagram, $P(A)=\frac{2}{7}$.

Step3: Identify the probability of event C given A

From the tree - diagram, when event A has occurred, the probability of event C is $P(C|A)=\frac{1}{3}$.

Step4: Calculate $P(A\cap C)$

$P(A\cap C)=P(A)\times P(C|A)=\frac{2}{7}\times\frac{1}{3}=\frac{2}{21}$.