Compute the Probability of Consecutive Heads in n Tosses
Company: Squarepoint
Role: Quantitative Researcher
Category: Statistics & Math
Difficulty: easy
Interview Round: Technical Screen
Find the probability that a sequence of n independent fair coin tosses contains at least one consecutive HH pair. Derive a recurrence and explain the connection to Fibonacci numbers.
### Constraints and Clarifications
The source uses a dice word while describing HH. This practice exercise explicitly interprets H and T as fair binary coin outcomes; a different outcome distribution requires a different recurrence. Let n be a nonnegative integer. The event is at least one adjacent HH occurrence, not exactly one occurrence.
### What a Strong Answer Covers
Count the complement with no adjacent heads, choose correct base cases, and divide by the number of equally likely sequences. Check small n before extrapolating a pattern.
### Follow-up Questions
- What changes when the probability of heads is p rather than1/2?
- Why are overlapping HH occurrences not independent events?
Overview: Derive the probability of at least one consecutive-heads pair by counting sequences that avoid HH. Establish the Fibonacci indexing, verify small cases, and extend the recurrence to a biased coin.
Read the full Squarepoint Quantitative Researcher interview experience this question came from