Imagine that you are looking at one cancer cell under the microscope, and trying
to estimate the probability that it will die due to a chemotherapy regime. You
know that 95% of cells treated with the chemotherapy turn on the P53 gene and
that these cells have 80% chance of dying. The remaining 5% do not turn on
P53 and have only 10% chance of dying. What is the probability that the cell
you’re looking at will die?
76.5%
66.5%
86.5%
69.75%
Cancer Cell Death Probability: P53 Gene Activation in Chemotherapy
Direct Answer
The probability that the observed cancer cell dies due to chemotherapy is 76.5%. This result comes from applying the law of total probability to the two mutually exclusive P53 activation scenarios.
Problem Breakdown
Under chemotherapy, 95% of cancer cells activate the P53 tumor suppressor gene, which triggers apoptosis with an 80% success rate in those cells. The remaining 5% fail to activate P53 and only die at a 10% rate, reflecting lower sensitivity to the drug. P53 activation serves as the partitioning event, making this a classic conditional probability setup relevant to CSIR NET Life Sciences exam questions on cell biology and cancer signaling.
Step-by-Step Calculation
Convert percentages to decimals: P(P53 on) = 0.95, P(die|P53 on) = 0.80, P(P53 off) = 0.05, P(die|P53 off) = 0.10.
First path: Probability of death via P53 activation equals 0.95 × 0.80 = 0.76.
Second path: Probability of death without P53 equals 0.05 × 0.10 = 0.005.
Total probability: 0.76 + 0.005 = 0.765 or 76.5%.
Option Analysis
- 76.5%: Correct – matches exact total probability calculation (
0.95×0.80 + 0.05×0.10 = 0.765). - 66.5%: Incorrect – possibly from miscalculating as (95%×80% + 5%×10%)/100 without decimals, yielding ~0.665 error.
- 86.5%: Incorrect – might stem from inverting probabilities (e.g., 95%×90% + 5%×20%), unrelated to given data.
- 69.75%: Incorrect – could arise from averaging (80%+10%)/2 weighted wrongly as 0.95×0.80 – 0.05×0.10 = 0.6975 subtraction mistake.
Option Comparison Table
| Option | Calculation Error | Matches Data? |
|---|---|---|
| 76.5% | None | Yes |
| 66.5% | Percent mishandling | No |
| 86.5% | Inflated rates | No |
| 69.75% | Subtraction instead of addition | No |
