Starting With Heads

What this conditional-probability interview question tests

This is a medium-difficulty probability question that combines counting under constraints with conditional reasoning. It rewards candidates who can set up the problem systematically: identify valid sequences that satisfy a constraint, then use conditional probability to isolate a subset.

The core skill is recognizing when a problem calls for enumeration of constrained outcomes rather than direct formula application. You'll need to count the total number of valid sequences (those with no consecutive heads), then count how many of those start with heads, and form the ratio. Firms value clean problem decomposition and the ability to verify your logic on small examples before scaling up.

• Combinatorial counting with forbidden patterns
• Conditional probability and Bayes' theorem
• Recursive or dynamic-programming approaches to constrained sequences