Question
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?
Answer: Option D
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
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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
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