Problema Solution
Kylie is about to play Aidan in the best two-out-of three at horse. If the probability that Kylie wins an individual game against Aidan is 35%, what is the probability that Kylie will win? Express your answer as a percent rounded to the nearest tenth.
Answer provided by our tutors
the probability that Kylie wins an individual game against Aidan is 35%:
P(K) = 0.35
P(A) = 1 - 0.35
P(A) = 0.65 is the probability that Aidan wins
we will assume that there is not tie, either Kyle or Aidam wins an individual game.
let denote with:
K = Kylie wins an individual game
A = Aidan wins an individual game
Kylie is the winner is he wins at least 2 out of 3 games that is if the following events happen
KKA, KAK, AKK, KKK
P(KKA) = P(KAK) = P(AKK) = P(K)P(K)P(A) = 0.35*0.35*(1 - 0.35) = 0.35*0.35*0.65
P(KKK) = P(K)P(K)P(K) = 0.35*0.35*0.35 = 0.35^3
where KKA means Kyle wins the first 2 games and Aidan wins the last game, KKK mean that Kyle wins all 3 games
P(Kylie wins 2 our of 3 games) = P(KKA) + P(KAK) + P(AKK) + P(KKK) = 3*0.35*0.35*0.65 + 0.35^3
P(Kylie wins 2 our of 3 games) = 0.28175 or 28.18%.