A relation $r(A, B)$ in a relational database has 1200 tuples. The attribute $A$ has integer values ranging from 6 to 20, and the attribute $B$ has integer values ranging from 1 to 20. Assume that the attributes $A$ and $B$ are independently distributed. The estimated number of tuples in the output of $\sigma_{(A>10)\vee(B=18)}(r)$ is ________.

Given:

• Total number of tuples, $N = 1200$

• $A \in [6, 20]$, so the domain size of $A$ is $20 - 6 + 1 = 15$

• $B \in [1, 20]$, so the domain size of $B$ is $20 - 1 + 1 = 20$

1. Selectivity of condition $C_1: (A > 10)$:

   • Integer values satisfying $A > 10$ are $\{11, 12, \dots, 20\}$, which is $20 - 11 + 1 = 10$ values.

   • $P(C_1) = \frac{10}{15} = \frac{2}{3}$

2. Selectivity of condition $C_2: (B = 18)$:

   • Only 1 integer value satisfies $B = 18$.

   • $P(C_2) = \frac{1}{20}$

3. Selectivity of condition $C_1 \lor C_2$ (independent attributes):

   $$P(C_1 \lor C_2) = P(C_1) + P(C_2) - P(C_1) \times P(C_2)$$

   $$P(C_1 \lor C_2) = \frac{2}{3} + \frac{1}{20} - \left(\frac{2}{3} \times \frac{1}{20}\right) = \frac{40 + 3 - 2}{60} = \frac{41}{60}$$

4. Estimated number of output tuples:

   $$\text{Estimated tuples} = N \times P(C_1 \lor C_2) = 1200 \times \frac{41}{60} = 20 \times 41 = 820$$