Taking a Hint and Updating Mid-Question

An interviewer who says "are you sure about that?" or "what if I told you the dice aren't independent?" is almost never making small talk — they're handing you a hint, often because they can see you're heading toward a wrong answer or missing a piece of the setup. How you react to that hint is itself part of the evaluation, separate from whatever you say next.

Update, don't dig in and don't restart blindly

The failure mode on one end is defending your original answer against the hint — treating "are you sure?" as a challenge to win rather than as new information. The failure mode on the other end is panicking and throwing away everything you'd built so far to start over from zero, even the parts the hint didn't actually touch. The right response sits between the two: take the hint as a genuine update, figure out specifically what it changes, and revise only that part of your reasoning.

Concretely, this sounds like: "Good point — if the dice aren't independent, that changes how I'd compute the joint probability, but the rest of my setup still holds. Let me redo just that piece." This response shows you can isolate what changed instead of treating every hint as either irrelevant or catastrophic, which is exactly the skill of updating a trading view on new information without overreacting to it or ignoring it.

Example

Working through an expected-value calculation, a candidate assumes a fair coin. The interviewer asks, "what if it's not fair?" A strong response: "Then I'd need to use $p$ instead of 0.5 in the expectation — let me call the probability of heads $p$ and redo the calculation symbolically, so it still works for any bias." A weak response either insists the original answer was fine, or scraps the whole approach and starts hunting for a completely different method.