MathGrit
ProblemsTechniquesPricing
Sign inGet started
Back to problems

HMMT — Game Win by Two Points Probability

2050SpecialistCombinatoricsProbability

Harvard-MIT Mathematics Tournament

Daniel and Scott are playing a game where a player wins as soon as he has two points more than his opponent. Both players start at par, and points are earned one at a time. If Daniel has a $60\%$ chance of winning each point, what is the probability that he will win the game?
0 students attempted0% solvedRating 2050

Related practice paths

AIME PracticeInteger-answer practice for deeper multi-step problems.How to Qualify for AIMEScore goals, contest choice, and prep habits for AIME hopefuls.AIME Practice StrategyHow to improve accuracy on high-difficulty problems.

Ready to check your answer?

Create an account to submit answers, save history, and track your rating.

Progressive Hints

Unlock hints one at a time — each reveals a little more without spoiling the solution.

Step-by-Step Solutions1

Multiple solution approaches with detailed walkthroughs, unlocked after you solve the problem.

AI-Powered Grading

Instant feedback on your answer — handles fractions, decimals, and equivalent forms.

Curated problem bank

Supported tracks for AMC, AIME, MATHCOUNTS, and olympiad-style training, plus global problem sources like UKMT, Euclid, and Kangaroo.