Flashcards in L2 - Conditional Probability Deck (12)
What are Dependent Events?
- the occurrence of one affects the chances of occurrence of the other. If one event has occurred, the probability of the other event changes (it is higher or lower).
Ex: pick a card from a deck of 52:
A = card is a king or an ace; P(A) = 8/52
B = card is royal; P(B) = 12/52
P(A ∩ B) = 4/52
What is conditional Probability?
- the probability of
A given that B has happened:
- written P(A|B)
How is Conditional Probability calculated?
P(A|B) = (P(A ∩ B))/(P(B))
P(B|A) = (P(A ∩ B))/(P(A))
If events are independent what is the Conditional Probability?
P(A|B) = P(A)
Note the following important important property:
P(A|B) ≠ P(B|A)
For Dependent Event what does the Multiplication Rule become?
P(A ∩ B) = P(A|B) x P(B)
P(A ∩ B) = P(B|A) x P(A)
For Independent Events what does the Multiplication Rule become?
P(A ∩ B) = P(A) x P(B)
P(B|A) = P(B)
Using these formulas is the quickest way to figure out if two events are independent
What is Bayes Theorem?
P(A|B)= (P(A ∩ B))/(P(B)) = (P(B|A) x P(A))/(P(B))
As (P(A ∩ B)) = P(B|A) x P(A)
P(B|A)= (P(A ∩ B))/(P(A)) = (P(A|B) x P(B))/(P(A))
As (P(A ∩ B)) = P(B|A) x P(B)
What is Independence or Independent Events?
Independence has to do with the probability of
occurrence, events can occur at the same time. For
P(A|B) ≠ 0 and P(A ∩ B) ≠ 0
What are Mutually Exclusive Events?
- events cannot occur at the same time
- P(A|B) = 0 and P(A ∩ B) = 0
What is Marginal Probabilities?
main events or headings, the sum
P(male) = 0.22 + 0.24 + 0.06 + 0.08 = 0.6 = 60%
P(Economics) = 0.24+0.26 = 0.5 = 50%.
- This is the Sum or the various Joint Probabilities e.g. Sum of Male doing Economics plus Male doing Finance + Male doing Banking
What are Join Probability?
Joint probability: the cells
P(male ∩ Econ) = 360/1500 = 0.24