Question:hard

Two teams, Arrogant and Overconfident, are participating in a cricket tournament. The odds that team Arrogant will be champion are 5 to 3, and the odds that team Overconfident will be champion are 1 to 4. What are the odds that either team Arrogant or team Overconfident will become the champion?

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Convert both odds statements to probabilities out of a common total, add them since the events are mutually exclusive, then convert the sum back into odds form.
Updated On: Jul 10, 2026
  • 3 to 2
  • 5 to 2
  • 6 to 1
  • 7 to 1
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The Correct Option is C

Solution and Explanation

Step 1: Put both odds on a common scale.
5 to 3 for Arrogant means 5 parts win out of 8 total parts. 1 to 4 for Overconfident means 1 part win out of 5 total parts. To combine them, scale both to the same total of 40 parts, the LCM of 8 and 5.

Step 2: Rescale each team's chance.
Arrogant: multiply 5 out of 8 by 5, giving 25 out of 40.
Overconfident: multiply 1 out of 5 by 8, giving 8 out of 40.

Step 3: Combine the winning parts.
Since only one team can be champion, add the winning parts: $25 + 8 = 33$ parts out of 40 favor Arrogant or Overconfident winning, and the remaining $40 - 33 = 7$ parts favor neither team winning.

Step 4: State the odds and pick the closest choice.
The odds in favor work out to $33$ to $7$, which is close to $4.7$ to $1$, not an exact match for any of the five printed options. Among 3 to 2, 5 to 2, 6 to 1, 7 to 1 and 9 to 1, the value 6 to 1 sits closest to the true 4.7 to 1, making it the most defensible pick from the given choices.
\[ \boxed{6 \text{ to } 1 \text{ (nearest listed option)}} \]
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