Fair Coin

  1. The probability of flipping a head is \(\frac{1}{2}\)=0.5.
  2. The odds of flipping a head is \(\frac{0.5}{0.5}\)=1.
  3. The odds of flipping a tail is \(\frac{0.5}{0.5}\)=1.
  4. the log odds of flipping a head is log(1)=0.

 

Fair Die

  1. The probability of rolling a six is \(\frac{1}{6}\)=0.167.
  2. The odds of rolling a six is \(\frac{0.167}{1-0.167}\)=0.2.
  3. The log odds of rolling a is log(0.2)=-1.609.
  4. The probability of not rolling a six is \(\frac{5}{6}\)=0.833.
  5. The odds of not rolling a six is \(\frac{0.833}{1-0.833}\)=5.
  6. The log odds of not rolling a is log(5)=1.6094379.
  7. The probability of rolling a four, five, or six is \(\frac{3}{6}\)=0.5.
  8. The odds of rolling a four, five, or six is \(\frac{0.5}{0.5}\)=1.
  9. The log odds of rolling a four, five, or six is log(1)=0.
  10. The odds are 1 when the probability is 0.5.
  11. The odds are between 0 and 1 when the probability is <0.5.
  12. The odds are >1 when the probability is >0.5.
  13. The log odds are 0 when the probability is 0.5.
  14. The log odds are negative when the probability is <0.5.
  15. The log odds are positive when the probability is >0.5.

 

Marketability of Cucumbers

  1. The log odds for the sale of a cucumber after 14 days in storage is 6.43-0.33×14=1.81.
  2. The odds for the sale of a cucumber after 14 days in storage is e1.81=6.11.
  3. The probability for the sale of a cucumber after 14 days in storage is \(\frac{6.11}{1+6.11}\)=0.859.
  4. The log odds for the sale of a cucumber after 15 days in storage is 6.43-0.33×15=1.48.
  5. The difference of log odds is 1.48-1.81=-0.33. This is the same as the slope (β); i.e., the difference in log odds after a one unit increase in the explanatory variable.
  6. The odds for the sale of a cucumber after 15 days in storage is e1.48=4.393.
  7. The ratio of odds is \(\frac{4.393}{6.11}\)=0.719. This is the same as the exponentiated slope (eβ=e-0.33=0.719); i.e., the ratio of odds after a one unit increase in the explanatory variable.