Advanced Math/Maths


QUESTION: Sir pls help.. Thanks in advance
My friend and I are in a debate based on a problem containing probability.

what is the probability of guessing the correct out come of 14 football matches (28 unique teams) with 3 possible outcomes in each match (Win draw and loss)

my logic says it is 1/3^(14),
but he debates it is [(1/3)*(2/3)*(2/3)]^14

can you please tell me the solution.

ANSWER: Angel, I think you're right. Given that the 3 possible outcomes are equally probable and that the outcomes of the games are independent, then the probability of getting the correct answer for a given game is 1/3. For all 14 games, this would be (1/3^14.

---------- FOLLOW-UP ----------

QUESTION: Sir thanks a ton for the reply..
Sir does this seem logic?
See, basically, 1/3 is the probability of the outcome a person can predict, then the other 2/3's are the added probability that the other outcomes will be false... So basically when the other two outcomes are false only then is the prediction right. So for one prediction to be right... 1/3 x 2/3 x 2/3 is the probability. So for 14 matches it's ^14.

The logic doesn't hold, I'm afraid. For instance, the probabilities of guessing correctly and incorrectly on the same game are not independent; after all

(probability of guessing correctly) + (probability of guessing incorrectly) = probability of something happening = 1

so if you know one, you know the other. Your logic implies that all 3 possibilities (win, lose, draw) have to happen. Not true! Only one happens.

If for no other reason, you cannot multiply the probabilities since that implies the events are independent.

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randy patton


college mathematics, applied math, advanced calculus, complex analysis, linear and abstract algebra, probability theory, signal processing, undergraduate physics, physical oceanography


26 years as a professional scientist conducting academic quality research on mostly classified projects involving math/physics modeling and simulation, data analysis and signal processing, instrument development; often ocean related

J. Physical Oceanography, 1984 "A Numerical Model for Low-Frequency Equatorial Dynamics", with M. Cane

M.S. MIT Physical Oceanography, B.S. UC Berkeley Applied Math

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