Suppose Cameroon beats China 5 to 2 in Soccer. (a) What’s the conditional probability that Cameroon...
Suppose Cameroon beats China 5 to 2 in Soccer.
(a) What’s the conditional probability that Cameroon was always ahead.
(b) What’s the probability that Cameroon scored the first two goals?
(c) What’s the conditional probability that Cameroon was always ahead (from the opening goal) given that Cameroon scored the first two goals?
Homework Answers
a)
this is problem based on Bertrand's ballot theorem
p = 5 and q = 2
required probability = (p-q)/(p+q) = 3/7
b)
W - scored by Cameroon
L - scored by china
total number of ways to arrange 5 W and 2L = 7!/(5! *2!) = 21
number of ways to arrange when first two are WW = 5C2 = 10
hence required probability = 10/21
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