Concept of Odds in Favor and Against

Data Science and A.I. Lecture Series

Author: Bindeshwar Singh Kushwaha

Institute: PostNetwork Academy

Concept of Odds

Odds in Favor and Against

• Odds in Favor: Ratio of favorable cases to unfavorable cases:\[
  \text{Odds in favor of } A = m : (n – m)
  \]
• Odds Against: Ratio of unfavorable cases to favorable cases:\[
  \text{Odds against } A = (n – m) : m
  \]
• Relationship with Probability:
  • \(P(A) = \frac{m}{n}\)
  • \(P(\text{not } A) = 1 – P(A)\)

Examples

Example 1

Problem:

• Odds in favor of event \(A\) are \(4:3\).
• What is the probability of \(A\)?

Solution:

• Favorable cases: \(m = 4\)
• Unfavorable cases: \(n – m = 3\)
• Total cases: \(n = 4 + 3 = 7\)
• \(P(A) = \frac{m}{n} = \frac{4}{7}\)

Example 2

Problem:

• Odds in favor of \(A\) are \(4:3\).
• Odds against \(A\) are \(5:8\).

Solution:

• Odds in favor of \(A\):
  • \(m = 4\), \(n – m = 3\), \(n = 4 + 3 = 7\)
  • \(P(A) = \frac{4}{7}\)
• Odds against \(A\):
  • \(n – m = 5\), \(m = 8\), \(n = 5 + 8 = 13\)
  • \(P(A) = \frac{m}{n} = \frac{8}{13}\)

Example 3

Problem:

• If \(P(A) = \frac{3}{5}\), find:
  • Odds in favor of \(A\).
  • Odds against \(A\).

Solution:

• \(P(A) = \frac{m}{n} = \frac{3}{5}\), so:
  • \(m = 3\), \(n = 5\), \(n – m = 5 – 3 = 2\)
  • Odds in favor of \(A\): \(3 : 2\)
  • Odds against \(A\): \(2 : 3\)

PDF Presentation

Odds in Favor and Against

Video

Questions

Odds in Favor and Against Quiz

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