HTHT in 4 coin flips

This quant interview question is about basic probability of discrete events in a simple random experiment. It anchors core ideas of independence, identical distribution, and equally likely outcomes in a very concrete setting, which is why it appears often in quant prep material and real interviews. It is a clean way to see if a candidate really understands how randomness and structure interact.

It trains your ability to formalize a random process, identify independent trials, and correctly compute the likelihood of one specific outcome among many possible ones. You must translate an everyday description into a probabilistic model, keep track of all possibilities, and reason about how probabilities combine across stages of an experiment.

This matters for quant interviews because the same logic underpins pricing path-dependent derivatives, modeling sequences of market moves, and building simple Monte Carlo simulations. Interviewers want to see that you can manipulate probabilities of complex event patterns without confusion, since this is fundamental in trading, risk, and quantitative research roles.

What it tests

When dealing with independent, identically distributed random events (like coin flips), the probability of observing a specific ordered sequence is determined by multiplying the probabilities of each independent outcome. Since each event is independent and has the same probability, the total probability for a sequence of $n$ events is the product of the individual probabilities, or $p^n$ if each outcome has probability $p$. This holds because the independence ensures that the outcome of one event does not affect the others, and the uniformity of the distribution means every sequence is equally likely. The total number of possible sequences grows exponentially with the number of events, leading to each specific sequence having a probability that is exponentially small in $n$. This structure underlies all problems where you are asked for the probability of a particular sequence of independent, equally likely outcomes.