Save
Maths
Part 5: Probability
Save
Share
Learn
Content
Leaderboard
Learn
Cards (22)
A
table
of
outcomes
is a visual method of showing the possible results of two independent events.
Probability
=
A
p
p
e
a
r
a
n
c
e
s
o
f
r
e
q
u
i
r
e
d
o
u
t
c
o
m
e
T
o
t
a
l
n
u
m
b
e
r
o
f
p
o
s
s
i
b
l
e
o
u
t
c
o
m
e
s
\frac{Appearances\ of\ required\ outcome}{Total\ number\ of\ possible\ outcomes}
T
o
t
a
l
n
u
mb
er
o
f
p
oss
ib
l
e
o
u
t
co
m
es
A
pp
e
a
r
an
ces
o
f
re
q
u
i
re
d
o
u
t
co
m
e
Probability
represents the chance, or likelihood, of something happening
Relative frequency
is an estimate of outcomes using probability and is worked out from trials in an experiment
Something has
bias
when one outcome is more or less likely to happen than another.
Something is
unbiased
when each outcome is equally likely to happen.
Mutually exclusive
events = events that cannot occur at the same time.
In statistics, a
population
is the overall group of people, values or items that can be grouped by a common characteristic
Sampling methods make sure that a study avoids
bias
by choosing the items fairly.
3 main types of sampling:
Random
sampling
Systematic
sampling
Stratified
sampling
Random sampling
: each item in the population has an equal chance of being chosen for the sample
Systematic sampling
: the population is ordered and items are chosen at regular intervals
Stratified sampling
: used when the population can be split into sub-categories (or strata) with the same characteristic
When we take a sample of a population, the
size
of the sample will affect how
representative
it is.
A
Venn diagram
is a visual method of showing the relationship between sets
Intersect
in a venn diagram is the overlap between different sets
Union
in a venn diagram
is the parts in set A or set B or both
The
complement of set A
on a Venn diagram contains the numbers that are not in set A
Events are
independent
if the probability of one outcome occurring does NOT affect the probability of another outcome occurring e.g. rolling a dice
Events are
dependent
if the probability of one outcome occurring DOES affect the probability of another outcome occurring.
AND
rule
P(A and B) =
P
(
A
)
⋅
P
(
B
)
P\left(A\right)\cdot P\left(B\right)
P
(
A
)
⋅
P
(
B
)
Events are
mutually exclusive
if they cannot both happen