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.
Your answer is correct , provided you have explained the problem correctly.
Your friend got his answer by multipling the probability of the chosen team winning by the independent probability of the other team not winning, but you can only multiply probabilities in this way if the events are independent . Clearly , they are not. To find the probability of two events, a and b , occuring, you multiply the probability of event a by the probabilty of event b , assuming that a has occured. If the chosen team wins, the probabilty of the other team having lost is equal to 1 , draw probabilty is equal to 0 . So , to do it your friend's way , you must multiply [(1/3)*(1)]^14 , which will give you your answer back again.