1
Sample Spaces
•
Sample space
, S, is set of all possible outcomes
of an experiment
Coin flip:
S = {Head, Tails}
Flipping two coins:
S = {(H, H), (H, T), (T, H), (T, T)}
Roll of 6sided die:
S = {1, 2, 3, 4, 5, 6}
# emails in a day:
S = {
x

x
Z,
x
≥ 0}
(nonneg. ints)
YouTube hrs. in day:
S = {
x

x
R
, 0
x
24}
Events
•
Event
, E, is some subset of S
(E
S)
Coin flip is heads:
E = {Head}
≥ 1 head on 2 coin flips:
E = {(H, H), (H, T), (T, H)}
Roll of die is 3 or less:
E = {1, 2, 3}
# emails in a day
20:
E = {
x

x
Z
, 0
x
20}
Wasted day (>5 YT hrs.):
E = {
x

x
R
,
x
> 5}
Note: When Ross uses:
, he really means:
Set operations on Events
E
F
S
•
Say E and F are events in S
•
Say E and F are events in S
S = {1, 2, 3, 4, 5, 6}
die roll outcome
E = {1, 2}
F = {2, 3}
E
F = {1, 2, 3}
Set operations on Events
E
F
S
E
F
Event that is in E or
F
•
Say E and F are events in S
S = {1, 2, 3, 4, 5, 6}
die roll outcome
E = {1, 2}
F = {2, 3}
E F = {2}
Note:
mutually exclusive
events means E F =
Set operations on Events
E
F
S
E
F
or
EF
Event that is in E and
F
•
Say E and F are events in S
S = {1, 2, 3, 4, 5, 6}
die roll outcome
E = {1, 2}
E
c
= {3, 4, 5, 6}
Set operations on Events
E
F
S
E
c
or
~E
Event that is not in E (called complement of E)
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