lecture 14

Question 1

describe ordinary probability

Answer 1

outcome must be an element in set S
only certain knowledge we have = outcome s is in S
we can then find P(A)
based on event of interest

Question 2

describe conditional probability

Answer 2

s is an element of B, B some or all in S
for some B, we know event B occurs
given B what do we now think about probability that A occurs also

Question 3

describe conditional probability - restrict

Answer 3

restrict parts of sample space
certain that sample outcome must lie in B
can forget about those outcomes not in B

Question 4

Conditional probability formula

Answer 4

FOR 2 events, A and B, conditional probability of A given B is denoted =
P(A|B)= P(A∩B)/P(B)
ONLY when P(B) >0

Question 5

Conditional probability - VENN diagram

Answer 5

now = B is entire possible collection
shrinks it down
knowledge of B affects what we think about A

Question 6

ex of conditional probability = dice roll

Answer 6

A∩B = 1/6 and P(B)=1/2
BUT
P(A|B)= P(A∩B)/P(B) = 1/6/1/2= 1/3

Question 7

what is keyword for conditional probability

Answer 7

GIVEN

Question 8

DESCRIBE WHAT happens when things equal each other - conditional probability

Answer 8

if B = S then P(A|S)= P(A∩S)/P(S) = P(A)/1 = P(A)
if B = A then P(A|A)= P(A∩A)/P(A) = P(A)/P(A)=1
therefore
P(A|B)= P(A∩B)/P(B) less than or equal to P(B)/P(B)=1

Question 9

WHAT is P(A∩B)

Answer 9

P(A∩B)=P(A|B)P(B)
where P(B)>0

Question 10

WHAT IS difference between P(A|B) and P(A∩B)

Answer 10

P(A∩B)= chance A and B occurs relative to S, A and B treated symmetrically in calculation
P(A|B) = chance of A and B OCCURIng relative to B, A and B not treated symmetrically - conditioning on event B

Question 11

what can knowledge of B do

Answer 11

could decrease, increase ot leave unchanged the probability of A occuring

Question 12

recall - simpsons paradox

Answer 12

was conditional probability
conditional probability given one event
then conditional prob given 2 events
paradox bc those 2 conditional probabilities are not comparable

Question 13

conditional probability rules

Answer 13

obeys probability rules
non negativity =
P(A|B)= P(A∩B)/P(B) greater than or equal to 0
for evENT S P(S|B)= P(S∩B)/P(B) = P(B)/P(B)=1
additivity =
P(A1 UNION A2 | B ) = P(A1|B) + P(A2|B)

Question 14

describe ex = failure of time of electrical component

Answer 14

A contained IN B if failed after 10 hours definitely failed after 5
if know lasts more than 5 hours = changes, chance of lasting more than 10 hrs increases