Answer: (1) 42%, (2) 60%, (3) 75%.
Step-by-step explanation: The calculations are as follows
(1) Given that
P(A) = 0.70, P(B) = 0.25 and P(A and B) = 0.30 ≠ 0. So, the conditional probability of even B when event A has already occured is given by
[tex]P(B/A)=\dfrac{p(B\cap A)}{P(A)}=\dfrac{0.30}{0.70}=0.42.[/tex]
Therefore, the answer is 42%. Also, since the intersection of A and B is not a null set, so these events are dependent events.
(2) Given that
P(A) = 0.40, P(B) = 0.60 and P(A and B) = 0.24 ≠ 0. So, the conditional probability of even B when event A has already occured is given by
[tex]P(B/A)=\dfrac{p(B\cap A)}{P(A)}=\dfrac{0.24}{0.40}=0.60.[/tex]
Therefore, the answer is 60%. Also, since the intersection of A and B is not a null set, so these events are dependent events.
(3) Given that
P(A) = 0.33, P(B) = 0.50 and P(A and B) = 0.25 ≠ 0. So, the conditional probability of even B when event A has already occured is given by
[tex]P(B/A)=\dfrac{p(B\cap A)}{P(A)}=\dfrac{0.25}{0.33}=0.75.[/tex]
Therefore, the answer is 75%. Also, since the intersection of A and B is not a null set, so these events are dependent events.
Thus, the answers are 42%, 602% and 75%.
