To find the conditional probability of event A given event B has occurred, we can use the formula for conditional probability:
[ P(A|B) = \frac{P(A \cap B)}{P(B)} ]
Given that the joint probability of events A and B is 32%, we have ( P(A \cap B) = 32\% = 0.32 ).
Given that the probability of event A is 60%, we have ( P(A) = 60\% = 0.60 ).
Given that the probability of event B is 50%, we have ( P(B) = 50\% = 0.50 ).
Substituting these values into the formula for conditional probability, we have:
[ P(A|B) = \frac{0.32}{0.50} \approx 0.64 ]
Therefore, the conditional probability of event A given event B has occurred is closest to 64.0%. Hence, the correct answer is option C.