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The cell cycle can be divided into two phases: interphase and mitosis (cell division). Mitosis is further subdivided into prophase, metaphase, anaphase, and telophase. A lab technician observed 200 cells from a cell line and recorded the number of cells in each phase of the cell cycle. The results are shown in the table.



\begin{table}

\captionsetup{labelformat=empty}

\caption{Number of Cells Observed (out of 200)}


Phase		Number of Cells Observed

interphase		170

prophase		20

metaphase		4

anaphase		2

telophase		4




\end{table}



Based on the data, what is the probability a randomly chosen cell will be observed undergoing cell division?


A15%
B18%
C30%
D85%

Verified Answer :

  • Identify the phases of mitosis: prophase, metaphase, anaphase, and telophase.
  • Sum the cells in these phases: \(20 + 4 + 2 + 4 = 30\).
  • Calculate the probability: \(P = \frac{30}{200} = 0.15\).
  • Convert to a percentage: \(0.15 \times 100\% = \boxed{15\%}\) (Option A).

Explanation

  1. Analyze the cell cycle data

To determine the probability that a randomly chosen cell is undergoing mitosis, we must first understand the classification of the cell cycle as provided. The total number of cells observed is \(N_{\text{total}} = 200\). According to the problem, the cell cycle is divided into interphase and mitosis. Mitosis itself consists of four distinct sub-phases: prophase, metaphase, anaphase, and telophase. Therefore, any cell observed in these four stages is currently undergoing mitosis.

  1. Calculate the number of cells in mitosis

We identify the number of cells in each phase belonging to mitosis:

  • Prophase: \(20\) cells
  • Metaphase: \(4\) cells
  • Anaphase: \(2\) cells
  • Telophase: \(4\) cells

To find the total number of cells in mitosis (\(N_{\text{mitosis}}\)), we sum these values:
\[N_{\text{mitosis}} = 20 + 4 + 2 + 4 = 30\]
So, there are \(30\) cells undergoing mitosis out of the \(200\) total cells observed.

  1. Calculate the probability and convert to percentage

The probability (\(P\)) that a randomly chosen cell is in mitosis is the ratio of the number of cells in mitosis to the total number of cells:
\[P = \frac{N_{\text{mitosis}}}{N_{\text{total}}} = \frac{30}{200}\]
To simplify this fraction, we can divide both the numerator and denominator by \(2\):
\[\frac{30 \div 2}{200 \div 2} = \frac{15}{100} = 0.15\]
To express this as a percentage, we multiply by \(100\%\):
\[0.15 \times 100\% = 15\%\]
Comparing this result to the given options, we find that it corresponds to option A.

Examples

This method of calculating phase percentages is a fundamental technique in histology and cytology. For instance, if you are studying tissue growth, you might use these counts to determine the "mitotic index"—the proportion of cells in a sample undergoing division—which helps researchers understand how rapidly a specific type of tissue is regenerating or growing. The calculation follows the simple ratio: \[ \text{Mitotic Index} = \frac{\text{Number of cells in mitosis}}{\text{Total number of cells}} \times 100\% \]

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