Probability

  • probability = preferred events / All events

  • Union is similar to ‘OR’ condition

  • Intersection is similar to ‘AND’ condition

  • Probability of getting event A or B is

    • P(A U B) = P(A) + P(B) - P(A and B)
    • We are subtracting P (A and B) because some elements will be common to both A and B and we will be double counting them. So we subtract P (A and B) to eleminate the double count

  • We can use Venn diagram to draw intersections, mutually exclusive probabilities etc. Venn diagrams can’t be used for conditional probabillity or to show dependence

  • We can use tree diagrams to visualize conditional probability and dependence

  • Probability of A given B - P(A | B)

  • If two probabilities are independent then:

    • P(A|B) = P(A) because A and B are independent and A does not depend on occurance of B, we can use this expression to check if two events are independent
    • P( A and B) = P(A|B)* P(B) as P(A|B) = P(A)
    • P(A and B) = P(A) * P(B) - when two events are independent then we need to multiply their probabilities
    • If two probabilities are independent then they are not mutually exclusive. If probabilities are mutually exclusive then they are not independent

  • Mutually exclusive events - Add the probabilities - P(A U B) = P(A) + P(B) because P(A and B) will be zero

Bayes Thereom

  • When we are provided information about a conditional probability eg P(A|B) and if we need to find the conditional probability P(B|A) then we should use Bayes theorem