Hello! It's time for another giveaway-- whoop whoop!
Your math question for today is
Suzy the Snowman and Douglas are playing tennis. It is currently a deuce (a tie), every ball Suzy has a 1/3 probability of winning and Douglas has a 2/3 probability of winning. The game is won when someone is ahead by more than two points. What is the probability that Suzy wins?
There is no limit in the rules to the number of times players can tie at deuce.
The clue said every ball Suzy has a 1/3 probability of winning and Douglas has a 2/3 probability of winning.
Every ball means at any time that the ball is being played.
The probability that Suzy wins= 1- Probability that Suzy lost = 1- Probability that Douglas won = Probability that Douglas lost given that when Suzy wins Douglas immediately lost.
The scenarios can be as followed:
One of the easiest outcomes is when Suzy won twice after the deuce: 1/3 x 1/3 = 1/9
However, this is just the beginning as Suzy can either win on her first-round or lose on her first round.
Hence, she could lose her first round but made a come back during the following two rounds: 2/3 x 1/3 x 1/3= 2/27
This could go on and on when Suzy win once and lose once in each of the game until she wins twice signalling her victory.
When rounding the probability of her winning to two decimal places you will get: 17.39%
I really would like to edit my post, but I don't know-how. Any way, I redo the work, I got 17.46 % as my finals answer her is what I did.
First I calculate the probability that Suzy win and Suzy lost ( W and L) which is 22 percent
Then I calculate the probability that Suzy win and win ( W and W) which is 11.11 percent
In this case , each loss would need to be compensated by the win and vice versa before ending with both win win.
Hence, what I did was that I multiplied 22% with 11.11% and multiply the result by two for the probability: (WIN LOSE WIN WIN or LOSE WIN WIN WIN)
You continue with this ( WIN LOSE WIN LOSE WIN WIN or LOSE WIN LOSE WIN WIN WIN) and then sums off of the possibility.
The number will become smaller as you go so rounding them to two decimal places will give you 17.46% .