Answer:
[tex]\sf P(B\;and\;D)=\dfrac{12}{35}[/tex]
Step-by-step explanation:
A tree diagram shows the probabilities for a sequence of two or more independent events.
The end of each branch is labelled with its outcome, and the probability of that event is written along the branch.
The 'AND' rule for probability states that P (A and B) =P(A) × P(B). Therefore, we multiply the probabilities along the branches:
[tex]\sf P(B\;and\;D)=\dfrac{4}{7} \times \dfrac{3}{5} \\\\\\ P(B\;and\;D)=\dfrac{4 \times 3}{7 \times 5} \\\\\\ P(B\;and\;D)=\dfrac{12}{35}[/tex]
So, the probability of events B and D is:
[tex]\Large\text{$\sf P(B\;and\;D)=\dfrac{12}{35}$}[/tex]
