Probability- Odds Question

Question

1. A confident and boastful coach claims that on the next league game the odds of her team winning are 3:1; the odds against losing are 5:1; and the odds against a tie are 7:1. Can these odds be right? Please show all work.

Answer 1

Let team has x wins, y loses and z ties.

Then we have system of equations: x/(y + z) = 3/1; y/(x + z) = 5/1 and z/(x + y) = 7/1;

We get system: x - 3y - 3z = 0; 5x - y + 5z = 0; 7x + 7y - z = 0 has only solution x = y = z = 0 because determinant of this system - 280 ≠ 0. So this situation impossible.