**Given Information:**

- p(A) = 2/3
- P(B) = 3/5
- P(AUB) = ?

**Calculating P(AUB):**

To calculate the probability of the union of two events (AUB), we can use the formula:

P(AUB) = P(A) + P(B) - P(A∩B)

Since P(AUB) is not given in the question, we cannot directly calculate P(A∩B) using the given information. Therefore, we need to have additional information or assumptions to proceed further.

**Calculating P(A/B):**

To calculate the probability of A given B (P(A/B)), we can use the formula:

P(A/B) = P(A∩B) / P(B)

Since P(A∩B) is not given in the question, we cannot directly calculate P(A/B) using the given information. Therefore, we need to have additional information or assumptions to proceed further.

**Calculating P(B/A):**

To calculate the probability of B given A (P(B/A)), we can use the formula:

P(B/A) = P(A∩B) / P(A)

Since P(A∩B) is not given in the question, we cannot directly calculate P(B/A) using the given information. Therefore, we need to have additional information or assumptions to proceed further.

**Calculating P(A/B) using Bayes' Theorem:**

If we assume that events A and B are independent, we can use Bayes' Theorem to calculate P(A/B).

Bayes' Theorem states:

P(A/B) = [P(B/A) * P(A)] / P(B)

Since we do not have the value of P(B/A), we cannot directly calculate P(A/B) using Bayes' Theorem. Therefore, we need to have additional information or assumptions to proceed further.

**Calculating P(AB):**

To calculate the probability of both A and B occurring (P(AB)), we can use the formula:

P(AB) = P(A) * P(B/A)

Since we do not have the value of P(B/A), we cannot directly calculate P(AB) using the given information. Therefore, we need to have additional information or assumptions to proceed further.

**Explaining P(A) * P(B) - P(AB):**

The expression P(A) * P(B) - P(AB) represents the probability of event A occurring (P(A)), multiplied by the probability of event B occurring (P(B)), minus the probability of both A and B occurring (P(AB)). This can be interpreted as the probability of A occurring but B not occurring.

However, without the values of P(A), P(B), and P(AB), we cannot calculate this expression using the given information alone. Additional information or assumptions are needed to determine the values of these probabilities and compute the expression.