statistics problem

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Question description

Who Will Win the Race?

Three runners, call them A, B, and C, are so well matched that in any race they have a 50-50 chance of beating either of the the other two runners.

Runner A wants to beat both B and C. Is it better for him to propose a 3-person race or to challenge each one to an individual race? Or does it not matter? Assume ties do not occur and fatigue is not a factor.

Hint: Use probabilities to come up with an answer.

Submit your answer on plain or lined paper with your name. To get full credit, you must show all your work in a logical approach that provides the correct answer. Typing is not required. Neat and legible work is a must!

It is a probability problem. To get full credit, I need to see the work that mathematically or logically leads me to an answer.

Who Will Win the Race? Three runners, call them A, B, and C, are so well matched that in any race they have a 50-50 chance of beating either of the the other two runners. Runner A wants to beat both B and C. Is it better for him to propose a 3-person race or to challenge each one to an individual race? Or does it not matter? Assume ties do not occur and fatigue is not a factor. Hint: Use probabilities to come up with an answer. Submit your answer on plain or lined paper with your name. To get full credit, you must show all your work in a logical approach that provides the correct answer. Typing is not required. Neat and legible work is a must!

DanielMax
School: UT Austin

Attached.

Solution
Since runners A, B and C each have a 50-50 chance of winning in a race, this implies that either
has a

1
3

probability of winning any race they jointly take part in as illustrated below.

Therefore, in this 3 person race, the probab...

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Anonymous
Wow this is really good.... didn't expect it. Sweet!!!!

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