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Joint Probability

  • A statistical measure where the likelihood of two events occurring together and at the same point in time are calculated. Joint probability is the probability of event Y occurring at the same time event X occurs.
  • Notation for joint probability takes the form:
    • P(X Y) or P(X,Y)
  • Which reads the joint probability of X and Y
  • The following table shows the joint probability of different events. Let’s say an economist is predicting the market scenario and the price of IBM stock from the next year.
  • Next year market can be Good, Bad or Neutral
  • IBM stock may go up or go down
  • Joint Probability Table:

Market

Good

Bad

Neutral

Total

IBM

UP

10%

30%

5%

45%

DOWN

0%

15%

40%

55%

Total

10%

45%

45%

100%

 

  • The probability of IBM stock being Up and Market being Good is 10%
  • Similarly, the probability of IBM stock being down and Market being neutral is 40% 

 

Conditional Probability

  • Probability of an event or outcome based on the occurrence of a previous event or outcome.  Conditional probability is calculated by multiplying the probability of the preceding event by the updated probability of the succeeding event
  • The probability of event A given that the event B has occurred is P(A/B), which is equal to the ratio of joint probability of A and B, and unconditional probability of B.
     
  • The unconditional probability of market being Neutral is 45%. Then using the table below we can find 3 conditional probabilities.
    • P(Up/Neutral) = 0.05/0.45
    • P(Up/Good) = 0.1/0.1
    • P(Down/Bad) = 0.15/0.45
    • Joint Probability Table:

 





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