Question

the diagram below represents an experiment consisting of two independent trials. find ( p(b \text{ and } c) ). ( p(b \text{ and } c)=\frac{?}{} )

Explanation:

Step1: Use the formula for independent events

For two independent events \( B \) and \( C \), \( P(B\cap C)=P(B)\times P(C|B)\). Since the trials are independent, \( P(C|B) = P(C)\) (the probability of \( C \) given \( B \) is just the probability of \( C \) in its trial). From the tree - diagram, \( P(B)=\frac{4}{7} \) and \( P(C)=\frac{2}{5} \).

Step2: Calculate the product

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Answer:

\(\frac{8}{35}\)