Two teams Arrogant and Overconfident are participating in a cricket tournament. The odds that team Arrogant will be champion is 5 to 3, and the odds that team Overconfident will be the champion is 1 to 4. What are the odds that either Arrogant or team Overconfident will become the champion?
Correct Answer: 33 to 7
As probability of a both the teams (Arrogant and Overconfident) winning simultaneously is zero.
$$\eqalign{ & P\left( {A \cap O} \right) = 0 \cr & P\left( {A \cap B} \right) = P\left( A \right) + P\left( B \right) \cr & = \frac{5}{8} + \frac{1}{5} \cr & = \frac{{33}}{{40}} \cr} $$
So required odds will be 33 : 7
$$\eqalign{ & P\left( {A \cap O} \right) = 0 \cr & P\left( {A \cap B} \right) = P\left( A \right) + P\left( B \right) \cr & = \frac{5}{8} + \frac{1}{5} \cr & = \frac{{33}}{{40}} \cr} $$
So required odds will be 33 : 7