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Compute Conditional Age Probability Among Cyclists

SIG (Susquehanna)Data Scientist · Online Assessment
EasyData ScientistOnline AssessmentStatistics & Math

Last updated

This question tests the ability to interpret a contingency table and calculate conditional probabilities by narrowing the sample space to a specific sub-group.

Problem Statement

A fitness tracking company surveys 1,000 individuals regarding their primary method of daily exercise and their age group. The data is summarized in the following contingency table:

Age GroupRunningBikingSwimming
18-301208545
31-5015011090
51+13073197

Given that a randomly selected person is a "Biking" enthusiast, what is the probability that they fall into the "31-50" age group? Express your answer as a simplified fraction.

Constraints

  • The calculations should be based strictly on the provided table.
  • The final result must be an irreducible fraction.

Example

If we wanted the probability that a person is in the "18-30" age group given they are a "Running" enthusiast:

  1. Total Running enthusiasts = 120 + 150 + 130 = 400.
  2. "18-30" Running enthusiasts = 120.
  3. Probability = 120 / 400 = 3/10.

Hints

Hint 1

Identify the total number of individuals who belong to the 'Biking' category across all age groups.

Hint 2

Identify the count of individuals who are specifically in the '31-50' age group AND choose 'Biking'.

Hint 3

Calculate the ratio of the count found in the second hint to the total found in the first hint, then simplify.

Follow-up questions

  • How would the calculation change if you were asked for the probability of being a 'Biking' enthusiast given the person is in the '31-50' age group?
  • What is the joint probability that a randomly selected person from the entire population is both a 'Biking' enthusiast and in the '31-50' age group?
  • If the 'Biking' category were redefined to include some 'Swimming' participants, how would that shift the conditional probability?