Odd Heads Up

Probability of an odd number of heads in fair coin flips

This is an easy probability question testing your ability to count outcomes and reason about symmetry. It's the kind of warm-up question interviewers use to establish baseline comfort with discrete probability before moving to harder problems.

The core skill is recognising the structure of the sample space—how many ways can you achieve each outcome, and what patterns emerge when you sum over a constraint like "odd number of heads". Most candidates solve this either by enumeration, by recognising a symmetry argument, or by thinking about the complementary event. Any rigorous approach works; the interview is really checking that you can set up and execute a clean calculation.

• Binomial coefficient counting
• Symmetry and complementary events
• Sample space exhaustion for small numbers of trials