Basic Probability Properties

Question 1

if the outcome if certain should experiments be carried out

Answer 1

no point

Question 2

what does the power set contain

Answer 2

all the events (subsets) and the empty set

Question 3

if the sample set has m elements, how many elements will the power set have, why

Answer 3

2^m

each sample point has the possibility of being included or not in the event so 2x2x2….x2

Question 4

what is the power set of

S ={1, 2}

Answer 4

P(S) = {null set, {1}, {2}, {1,2}}

Question 5

what are mutually exclusive events

Answer 5

events that cannot occur at the same time

where aNb =0

Question 6

what is the union of two mutually exclusive events

Answer 6

P(AuB)= P(A) + P(B)

Question 7

what does the notation

A^c represent

Answer 7

complement of A

everything but what is in A

Question 8

what is AnA^c always

Answer 8

0

Question 9

what is AuA^c always

Answer 9

sample space

Question 10

what is P(A)+P(A^c) always

Answer 10

1

Question 11

is it possible to define a probability on the power set of an uncountably infinite sample space

Answer 11

no

Question 12

example of an uncountable infinite set

Answer 12

probability of a dart landing on a specific point on a dart board as there are an infinite number of points it could land on

Question 13

what is an example of a countably infinite sample space

Answer 13

repeatedly tossing a coin until the first head shows up

could possibly be infinite

Question 14

how to find P(B|A)

conditional

Answer 14

P(B|A) = P(AnB)/P(A)

Question 15

if two probabilities are independent, what is the conditional probability

P(A|B)

Answer 15

P(A)

B does not effect A if they are independent

Question 16

what does it mean when two events are mutually exclusive

Answer 16

if B occurs then A cannot occur simultaneously

Question 17

for two mutually exclusive events, what is P(A|B)

Answer 17

0

Question 18

two events are independent if

P(AnB) =

Answer 18

P(A)P(B)