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

Step 1: Given probabilities.

P(A > 10) = 10 / 15
P(B = 18) = 1 / 20

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Step 2: Apply probability formula.
Assuming independence between attributes A and B:

P((A > 10) ∨ (B = 18)) = P(A > 10) + P(B = 18) − P(A > 10)P(B = 18)

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Step 3: Substitute values.

= (10 / 15) + (1 / 20) − (10 / 15)(1 / 20)

= 0.6667 + 0.05 − 0.0333

= 0.6834

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Step 4: Estimate number of tuples.
Total number of tuples = 1200

Estimated tuples = 1200 × 0.6834 ≈ 820

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Final Answer:

820