Expected Number of Runs in Coin Tosses
Last updated: September 2, 2026
Quick Overview
This question asks the candidate to calculate the expected number of runs in a series of coin tosses, specifically when tossing a coin 21 times.
Goldman Sachs
September 2, 20261
0
12 solved
This question asks the candidate to calculate the expected number of runs in a series of coin tosses, specifically when tossing a coin 21 times.
This question is typically asked during the online assessment round for data science roles at Goldman Sachs to evaluate a candidate's understanding of probability and statistics. Interviewers are looking for the candidate's ability to apply mathematical concepts to practical problems, as well as their analytical thinking skills in deriving expected values from random processes.
What the Interviewer Expects
- Define what a 'run' is in the context of coin tosses.
- Explain the formula for calculating the expected number of runs.
- Provide a step-by-step calculation for the expected number of runs in 21 tosses.
- Discuss any assumptions made during the calculation.
- Conclude with the final expected value.
Key Topics to Cover
How to Approach This
- Define your hypotheses (H0 and H1) clearly before performing any test.
- Calculate required sample size BEFORE running an experiment, using power analysis.
- Remember the Central Limit Theorem: sample means become approximately normal with large n.
- Watch for Simpson's paradox. Always segment data by key dimensions.
- Distinguish between statistical significance and practical significance.
Possible Follow-up Questions
- How would the expected number of runs change if the number of tosses increased?
- Can you explain how this concept applies to other random processes?
- What are the implications of this calculation in real-world scenarios?
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To solve the problem of finding the expected number of runs in 21 coin tosses, we first need to define what a 'run' is. A run is a sequence of consecutive identical outcomes in a series of trials. For...
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