462.Penalty Kicks and Pólya's Urn
★★★conditional probabilityCh. 2 — Axiomatic and Conditional Probability444+ Problems in Probability
You take 100 penalty kicks. You made kick 1 and missed kick 2. From kick 3 on, the probability you score equals the fraction of kicks scored so far (if you made 17 of the first 30, you make kick 31 with probability ). What is the probability that you score exactly 66 of the 100 kicks?
Sign in to submit an answer and track it toward your stats.
Sign inHint
This is a Pólya urn. Work out the distribution of the final tally for a small case — say 4 kicks — and guess the pattern.
Want timed drills, mental math, and a market-making game too? Try the full practice suite →