Lecture 6

Question 1

unconditional probability

Answer 1

no special conditions are assumed other than those that define the experiment

Question 2

conditional probability (and formula)

Answer 2

additional knowledge might affect the outcome of the experiment, and the probability of the event of interest may need to be altered

P(A|B) = P(A backwards U B)/P(B)
P(B|A) = P(A backwards U B)/P(A)

Question 3

multiplicative rule of probability

Answer 3

multiplying both sides of conditional probability equation by the P(A) gives a formula for the probability of the intersection of two events

P(A backwards U B)= P(B) P(A|B)
P(A backwards U B)= P(A) P(B|A)

Question 4

independent events

Answer 4

two events A and B are said to be independent if the occurrence of event B does not alter the probability that A has occurred and vice versa
(i) P(A|B) =P(A)
(ii) P(B|A) = P (B)
(iii) P(A backwards U B)= P(A) P(B)

events that are not independent are said to be dependent

Question 5

the property of independence cannot be show on a …

Answer 5

venn diagram

Question 6

Why are mutually exclusive events dependent?

Answer 6

If A and B are mutually exclusive events with nonzero possibilities, then the assumption that B occurs means it is impossible for A to have occurred simultaneously (P(A|B)=0).

Question 7

if events A and B are independent then…

Answer 7

the probability of the intersection of A and B is P(A backwards U B)= P(A) P(B). The converse is also true, if P(A backwards U B)= P(A) P(B), then events A and B are independent.