Two players play independent games of table tennis.
-
Player A wins each game with probability
p
(constant across games).
-
They play a
best-of-5
match (first to 3 wins).
-
Let
X
be the
number of games played
until the match ends (so
X∈{3,4,5}
).
Tasks
-
Compute
θ=Pr(X=5)
.
-
Write a simulation (Monte Carlo) approach to estimate
θ
.
-
Follow-up: given
M
simulated matches, how would you build a
confidence interval
for
θ
?