SOLUTION: Please Help, I'm so confused on how to even start. Thanks! Homework question: 2 teams: Boston Celtics and Denver Nuggets Home team has 60% chance of winning; away team h

Click here to see ALL problems on Probability-and-statistics

Question 129233: Please Help, I'm so confused on how to even start. Thanks!
Homework question:
2 teams: Boston Celtics and Denver Nuggets
Home team has 60% chance of winning; away team has 40% chance of winning.
What is the probability the Celtics will win the Championship at 4:2 out of 6 games:
1.) Draw the probability tree of the problem to explain answer?
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
2 teams: Boston Celtics and Denver Nuggets
Home team has 60% chance of winning; away team has 40% chance of winning.
What is the probability the Celtics will win the Championship at 4:2 out of 6 games:
1.) Draw the probability tree of the problem to explain answer?
------------------------------
1st Root: Celtics
two branches: win with a probability of 3/5; lose with a prob. of 2/5
Each of those branches has two branches:
P(win|win)=(3/5)^2;
P(lose|win)=(3/5)*(2/5)= 6/25
-----------
Then each of those brances has two branches
Comment: This continues till you have 6 games.
--------
You want the sum of the probabilities illustrating 4 Celtic wins and 2
Denver loses.
--------------------
Each branch has probability (3/5)^4(2/5)^2; and there are 15 such branches.
Since the events illustrated by all those branches are mutually exclusive
(one cannot be the other) the sum of the probabilities is 15(3/5)^4(2/5)^2
= 0.31104
=====================
Cheers,
Stan H.