Question

Assume that the human haploid genome is \(3 \times 10^{9}\) base pairs long. The mutation rate, when DNA is copied, is \(5 \times 10^{-11}\) per base pair per replication. Based on these numbers, the expected number of mutations that take place per replication of the human haploid genome is _______ (Round off to two decimal places)

Hint:

Multiply the total genome length in base pairs by the per-base-pair mutation rate: (3 x 10^9) x (5 x 10^-11).

Answer 1

Correct Answer: 0.15

Step 1: Understanding the Question.
We are given the total length of the human haploid genome, \(3 \times 10^{9}\) base pairs, and the mutation rate per base pair per replication, \(5 \times 10^{-11}\). We need to find the expected total number of mutations across the whole genome each time it is copied.

Step 2: Key Formula or Approach.
The mutation rate given is a per-base-pair probability of a mutation occurring during one replication. To get the expected number of mutations across the entire genome, we treat each base pair as an independent trial with this small probability of mutating, and simply multiply the mutation rate by the total number of base pairs (this is the expected value of a sum of many independent, low-probability events):
\[ \text{Expected mutations} = (\text{genome length in base pairs}) \times (\text{mutation rate per base pair}) \]

Step 3: Detailed Explanation.
Substituting the given values:
\[ \text{Expected mutations} = (3 \times 10^{9}) \times (5 \times 10^{-11}) \]
First multiply the coefficients: \(3 \times 5 = 15\).
Then combine the powers of ten: \(10^{9} \times 10^{-11} = 10^{-2}\).
\[ \text{Expected mutations} = 15 \times 10^{-2} = 0.15 \]
This is already at two decimal places, so no further rounding is required.

Step 4: Final Answer.
The expected number of mutations per replication of the human haploid genome is 0.15.
\[ \boxed{0.15} \]