Question

A relation \( r(A,B) \) has 1200 tuples. 
Attribute \( A \) ranges from 6 to 20 and attribute \( B \) ranges from 1 to 20. Assume independent uniform distribution. The estimated number of tuples in \( \sigma_{(A>10)\vee(B=18)}(r) \) is \(\underline{\hspace{2cm}}\).

Hint:

For OR conditions, always subtract the intersection probability.

Answer 1

Correct Answer: 819 - 820

\[ P(A>10) = \frac{10}{15}, P(B=18) = \frac{1}{20} \] \[ P((A>10)\vee(B=18)) = P(A>10) + P(B=18) - P(A>10)P(B=18) \] \[ = \frac{10}{15} + \frac{1}{20} - \frac{10}{15}\times\frac{1}{20} \] \[ = 0.6667 + 0.05 - 0.0333 = 0.6834 \] \[ \text{Estimated tuples} = 1200 \times 0.6834 \approx 820 \] Final Answer: \[ \boxed{820} \]