# statistics problem

**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.**

## Tutor Answer

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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