A football match may be either won,draw or lost by the host country's team. So there are 3 ways of forecasting the result of any one match. What is the probability of forecasting at least 3 out of 4 matches?

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Answer 1 · 2018-05-30T07:47:55

#1/9=11.bar1%#

We can solve this using binomial probability. When starting a question like this, I like to start with this relation:

#sum_(k=0)^(n)C_(n,k)(p)^k(1-p)^(n-k)=1#

We have 4 matches: #n=4#.

The probability of forecasting a match correctly is #1/3# (there are 3 possible ways of forecasting and only 1 way of being right).

We're looking at getting at least 3 correct, so that's #3<=k<=4#:

#C_(4,3)(1/3)^3(2/3)^(1)+C_(4,4)(1/3)^4(2/3)^(0)#

#=4(2/81)+1(1/81)=9/81=1/9#