Kate's Chances of Winning a 5 Match Tennis Tournament

[Bushy]

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?

 

[Prove It]

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).

 

[Bushy]

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 ?

 

[Prove It]

Therefore 0.8^3 / 0.8^3 = 1 ?

NO! The top is the probability of winning all FIVE!

 

[Bushy]

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?

 

[Prove It]

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!