A football team, LIBO, wins a match with probability 0.75 irrespective of its opponents. What is the probability that the team wins 4 matches out of 5 matches?
In a knockout tournament, LIBO faces a series of opponents until it loses to someone. How many matches does LIBO expect to play before it gets eliminated from the tournament?
If LIBO is already in Quarter final, what is the probability that it's going to play the Final and becomes Champion?
For the solution what i've assumed
(a)${5 \choose 4} (0.75)^4 (1-0.75)$
(b)$E[N] = \sum_{i = 0}^{n}i(0.75)^i(1-0.75)^{n-i}$
(c) $P(A|B) = \frac{P(AB)}{P(B)}$
But i'm not sure how to solve the (b) and (c) one.
For (b), $$E[N] = \sum_{i=1}^\infty i P(N=i).$$ What is $P(N=i)$ (probability of playing $i$ matches before being eliminated)? They need to win $i-1$ matches and lose the last one.
For (c), you don't need conditional probability. They just need to win three matches (assuming it's a single-elimination tournament bracket).