statistics problem

statistics problem

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.