Conditional Probability

Write the probability of any E for sample space S symbolically

P(E) = |E| / |S|

T/F - P(E) = 1.05

False

For any event E, P(E) ∈ [0, 1]

Write the probability of any E given E^C symbolically

P(E) = 1 - P(E^C)

T/F - P(E ∪ F) = P(E) + P(F)

False

P(E ∪ F) = P(E) + P(F) - P(E ∩ F)

[Otherwise, P(E ∩ F) counted twice in sum]

Write the probability of any A given B symbolically

P(A | B)

Find the probability of spinning both odd numbers on a 5-slice spinner given the sum of the spins being less than 5

3/6

Find the probability of drawing a face card from a standard deck of 52 given the card is red

6/26

Find the probability of P(A | B) given the probability of individual sets

P(A | B) = P(A ∩ B) / P(B)

independent events

P(A | B) = P(A)

T/F - Given the following, A and B are independent events

P(A) = 0.5

P(B) = 0.12

P(A ∩ B) = 0.6

False

P(A | B) ≠ P(A)

Differentiate independent events from mutually exclusive events

• independent events describe set probabilities

• mutually exclusive events describe set intersections

Find P(A | B) given that A and B are mutually exclusive events

P(A | B) = 0

P(A | B) given that B is a subset of A

P(A | B) = 1

Law of total probability

P(A) = P(A ∩ B) + P(A ∩ B^C)

Law of total probability in terms of conditional probability [ Show proof ]

P(A | B) = P(A ∩ B)/P(B)

P(A | B)P(B) = P(A ∩ B)

P(A) = P(A | B)P(B) + P(A | B^C)P(B^C)