(Image removed from quote.)
i dont get ques 4ii)
the ans is written below
Hey again!
This is a
Bernoulli Trial, so we could consider the different ways it can happen using the Binomial distribution. However, we have to consider the fact that the number of trials changes based on the events to that point. That said, for me, it is easier to break it down into the 3 possibilities: 3 sets played, 4 sets played, or 5 sets played.
3 sets played is an easy one, Novak must win in straight sets:
For the rest, we need to adjust our thinking. If they are playing
until three sets are won, and we are considering Novak winning, then that means Novak must win the last game.
So, for when we want to consider the probability of winning in 4 sets, we only need to consider a Bernoulli Trial with 3 sets, because we know the fourth will be won by Novak.
So we take the appropriate term from here, and multiply by 2/3 to consider the probability of Novak winning the 4th set. So it's binomial distribution for the first 3 sets, then just basic probability in the fourth, because we know Novak needs to win it:
This corresponds to the second term of your answer (I think there is a dictation error in the solution, because it out by a multiple of 2/3.
We do the same thing for winning in 5 sets; consider the binomial probability of Novak winning 2 sets out of 4 (since we don't know the order), and then multiplying by 2/3 to consider the probability of him winning in the 5th. This corresponds to the last term of your answer, and if you add everything together, you get the answer
I hope that helps!!