Compute Conditional Age Probability Among Cyclists
Company: Sig
Role: Data Scientist
Category: Statistics & Math
Difficulty: easy
Interview Round: Online Assessment
# Compute Conditional Age Probability Among Cyclists
One thousand survey participants reported a preferred exercise method. Results are grouped by age:
| Exercise | 18–22 | 23–27 | 28–32 | 33–37 | Total |
|---|---:|---:|---:|---:|---:|
| Run | 54 | 40 | 42 | 66 | 202 |
| Bike | 77 | 68 | 90 | 70 | 305 |
| Swim | 28 | 43 | 50 | 52 | 173 |
| Other | 90 | 78 | 71 | 81 | 320 |
| Total | 249 | 229 | 253 | 269 | 1,000 |
A uniformly selected survey participant is known to prefer biking. What is the probability that the participant is between 23 and 27 years old? Express the answer as a fraction in simplest form.
### What a Strong Answer Covers
- Identification of the biking row as the conditioned sample space.
- The correct joint cell and row total.
- Fraction simplification and an explanation of why the overall survey total is not the denominator.
### Follow-up Questions
- What is the probability that a participant prefers biking given that they are 23–27?
- Are the events “prefers biking” and “is 23–27” independent in this table?
Overview: Compute a conditional probability from a complete age-by-exercise contingency table. The answer selects the biking row as the conditioned population, derives 68/305, confirms the fraction is reduced, and distinguishes conditional, reverse-conditional, and joint probabilities.
Read the full Sig Data Scientist interview experience this question came from