Give the correct numerical response. If $A$ and $B$ are events, with $P(A)=\frac{1}{5}$ and $P(B)=\frac{2}{3}$, and $P(A$ and $B)=\frac{1}{3}$, then $P(A$ or $B)$ is If $A$ and $B$ are events, with $P(A)=\frac{1}{5}$ and $P(B)=\frac{2}{3}$, and $P(A$ and $B)=\frac{1}{3}$, then $P(A$ or $B)$ is (Simplify your answer.)

Step 1 ：Given that the probability of event A, denoted as P(A), is \(\frac{1}{5}\) or 0.2, the probability of event B, denoted as P(B), is \(\frac{2}{3}\) or approximately 0.6667, and the probability of both events A and B occurring, denoted as P(A and B), is \(\frac{1}{3}\) or approximately 0.3333.

Step 2 ：We can calculate the probability of either event A or event B occurring, denoted as P(A or B), using the formula: P(A or B) = P(A) + P(B) - P(A and B).

Step 3 ：Substituting the given values into the formula, we get P(A or B) = 0.2 + 0.6667 - 0.3333.

Step 4 ：Simplifying the above expression, we find that P(A or B) is approximately 0.5333.

Step 5 ：Final Answer: The probability of either event A or event B occurring is \(\boxed{0.533}\).