Kate's Chances of Winning a 5 Match Tennis Tournament

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Discussion Overview

The discussion revolves around the probability of Kate winning a 5 match knockout tennis tournament, given her individual match win probability of 80%. Participants explore the calculations for her overall chances of winning the tournament and the conditional probability of winning the tournament after winning her first three matches.

Discussion Character

  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • Some participants propose that the probability of Kate winning the tournament is calculated as 0.8^5, which they equate to 33% or 1024/3125.
  • There is a discussion about the conditional probability of winning the tournament given that she wins her first three matches, with some suggesting it is the same as the overall probability.
  • One participant questions whether the intersection of winning the first three matches and winning all five matches should be considered as simply winning the first three matches.
  • Another participant argues that winning all five matches inherently includes winning the first three matches, leading to confusion about the interpretation of the intersection of these events.

Areas of Agreement / Disagreement

Participants express differing views on the interpretation of the intersection of probabilities related to winning matches, leading to an unresolved debate on the correct approach to calculating the conditional probability.

Contextual Notes

Participants do not reach a consensus on the correct interpretation of the intersection of probabilities, and there are unresolved mathematical steps regarding the conditional probability calculations.

Bushy
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The Probability of Kate winning a tennis match is 80%. If she enters a 5 match knockout tournament, find the chance of her:

a) winning the tournament:

Is simply 0.8^5 = 33%

b) winning the tournament given she wins her first three games:

Is the intersection of the two over the probability she wins the first three = 0.8^5 * 0.8^3 / 0.8^3 = the same as part a?
 
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Bushy said:
The Probability of Kate winning a tennis match is 80%. If she enters a 5 match knockout tournament, find the chance of her:

a) winning the tournament:

Is simply 0.8^5 = 33%

Keep your answer exact please. $\displaystyle \begin{align*} \left( \frac{4}{5} \right) ^5 = \frac{1024}{3125} \end{align*}$.

b) winning the tournament given she wins her first three games:

Is the intersection of the two over the probability she wins the first three = 0.8^5 * 0.8^3 / 0.8^3 = the same as part a?

No, winning all five and winning the first three is equivalent to simply winning all five. So the intersection is simply what you found in part (a).
 
Prove It said:
No, winning all five and winning the first three is equivalent to simply winning all five. So the intersection is simply what you found in part (a).

Therefore 0.8^3 / 0.8^3 = 1 ?
 
Bushy said:
Therefore 0.8^3 / 0.8^3 = 1 ?

NO! The top is the probability of winning all FIVE!
 
Well that would give a neat answer, but aren't we saying the intersection of winning the first three and winning all five should be winning the 1st three?
 
Bushy said:
Well that would give a neat answer, but aren't we saying the intersection of winning the first three and winning all five should be winning the 1st three?

No, the only way it is possible to do both "winning all five games" and "winning the first three games" is to win all five games!
 

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