Which method do should I use?

2

2soon

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Joined
Dec 16, 2019
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Hi,

Assuming 6 tennis matches with different levels of skill, which method should I use to work out the chances of 4 of my predictions winning.

For example,

Game 1 i predict player a has a 67% chance of winning,

Game 2 55% chance

Game 3 77% chance

Game 4 32% chance

Game 5 10% chance

Game 6 89% chance

And I wish to work out the percentage chance of predicting, 1,2,3,4,5,6

I tried using factorials but obv that doesn't work or I am using it incorrectly.

Thanks
 
It's good you discovered that "using factorials" doesn't help.

You could draw a tree. That will be fun.

Game 1 0.67 vs 0.33
Game 2 after Game 1 Correct
0.67 * (0.55 vs 0.45) ==> 0.67*0.55 two correct, 0.67*0.45 still one correct
Game 2 after Game 1 Incorrect
0.33 * (0.55 vs 0.45) ==> 0.33*0.55 one correct, 0.33*0.48 still zero correct

After two games, there are four paths. How many will there be after 6 games?
 
Agreed, a tree is a good option.

The problem I have is there could be up to 300 different games and I am looking at running this through excel and typing out the code for all the tree is going to be a nightmare everyday.

Any ideas for a different method I could use?
 
well... what you need to do is for say k=3

list all the triplets possible from the 6 games.
Each triplet represents the games you correctly predict win.
The probability of one of these is the percentages you specified for each of the winning games
And 1 minus these percentages for the losing games.

For example P[(1,3,5) ] = (0.67)(1-0.55)(0.77)(1-0.32)(0.10)(1-0.89)
P[k=3]= the sum of all these products across all the triplets.

Do this for k=0,6

I suggest software.
 
2soon said:
I'm not sure I understand, or I'm not explaining myself properly....

The chance of hitting one of six should be higher than than the chance of hitting two from six.
Click to expand...

Note these number are for exactly k correctly predicted wins. Not at least k.
 
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