90. Assuming equal frequency for all 4 nucleotides ( G, A, T, C ), how many EcoRI recognition sites
(GAATTC) are possible in a bacterial artificial chromosome of 100,000 base pairs?
(A) 6
(B) 12
(C) 24
(D) 48

EcoRI recognizes the specific 6-base pair sequence GAATTC, and in random DNA with equal nucleotide frequencies, the expected number of such sites in a 100,000 bp bacterial artificial chromosome (BAC) is approximately 24.[web:4]

Calculation Method

The probability of the GAATTC sequence occurring at any position is (1/4)^6 = 1/4096, since each of the 6 nucleotides has a 1/4 chance.[web:4] In a 100 kb sequence, there are effectively 100,000 – 5 = 99,995 possible starting positions for a 6-bp site, but for large N, this approximates to 100,000.[web:4] Thus, expected sites = 100,000 / 4096 ≈ 24.41, which rounds to 24 as the closest integer among options.[web:4]

Option Analysis

• (A) 6: This underestimates severely; it might assume a shorter sequence like 25 kb (25,000/4096 ≈ 6), not 100 kb.[web:4]
• (B) 12: Matches roughly half the length, e.g., 50 kb (50,000/4096 ≈ 12), ignoring full BAC size.[web:4]
• (C) 24: Correct, as 100,000/4096 ≈ 24, standard statistical expectation for random DNA.[web:4]
• (D) 48: Overestimates, perhaps doubling without accounting for exact math (200,000/4096 ≈ 48).[web:4]