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 âˆ©Y) or P(X,Y)
- Which reads the joint probability of X and Y
- The following table shows the joint probability of different events. Letâ€™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: