# 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:
• 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