5. 1 THE PROBABILITY OF AN EVENT 5.5 ADDING PROBABILITIES
" "
OR
•
probability : proportion of times the event would occur if we repeated a random trial over and •
to get the probability that we get either one ev
over again under the same conditions .
Probability =
between 0 and 1 .
ex ) Pr that a person has blood type 0 =
Pr of e
↓
never atways
PREA ] :
probability of event A. Addition Rule : If 2 events are mutually exclusi
•
random that :
process that has two or more possible outcomes whose occurrence cannot the sum Of probabilities of each separately .
be prldlcted WI certainty .
Pr [ 0
-
or Ot ] = 0.374 t 0-066 =
0.440
'
ex ) flipping a coin , rolling a pair Of dice to see their sum . Pressing Shuffle
'
0h MUSIC .
biological :
randomly sampling 10 babies to see If female ( 1/2 ) Probabilities Of all possible mutually exclusive outcom
event of Interest :
any potential subset of all Possible Outcomes Of a random that ex ) blood type 8 outcomes
• .
=
" ' "
ex ) rolling a cue : result Is an even # ! result IS four " Pr [ Ot or 0
-
or At or A- or Bt or B- Or ABT or AB
•
possible outcomes : all outcomes In a trial .
•
Pr [ not A ] =
I -
Pr [ A ]
"
"
ex ) rolling a die : numbers I -6
General Addition Rule
5. 2 VENN DIAGRAMS • If events are not mutually exclusive : person to
•
probability of an event Is proportional to the area It Occupies In the diagram . Pr [ A ORB ] =
Pr EA ] t Pr [ B ] -
Pr [ A and B ]
M r = 0 If
/
-
Prca etting > 2) : 416=213 -
calculates probability that either A Or B ( or both
/
-
/ : .
If Pr [ A and B ] not subt
5. 3 MUTUALLY EXCLUSIVE EVENTS
•
two events that cannot both occur at the same time .
Pr [ A and B] = 0 5.6 INDEPENDENCE & MULTIPLICATION RULE
' '
independent If the occurrence of
'
ex ) events one and SIX
'
bc One die cannot produce both two events are
mutually exclusive
•
are .
probability that the other will also occur . ex ) roll
5. 4 PROBABILITY DISTRIBUTIONS •
If occurrence of one event provides at least som
•
describes the probability of each of the possible mutually exclusive outcomes of a random that . two events are dependent
Discrete Probability Distribution Multiplication Rule
-
for categorical and discrete numerical variables •
for independent events ,
Pr that they both occur
-
equally probable outcomes ( G- = 0.167 ) Pr [ A and B ] = Pr [ A] .
Pr [B ]
sum of all probability 1 ( probability of some OUTCOME OCCUR ) f- f- ¥
" "
3]
=
ex ) Pr [ 1st roll is 3 and 2nd roll
=
-
. IS = ✗
Continuous Probability Distributions
•
continuous numerical variables can take on any real # Value within some range .
•
height Of curve : probability density Independence Of More than TWO Events
•
can describe probability of any range of Values for Y .
ex ) Chance Of Offspring being green = 314 . Chanc
•
height of cont .
probability curve does NOT give the probability what IS the chance of all 10 Offspring s being gree
" "
OR
•
probability : proportion of times the event would occur if we repeated a random trial over and •
to get the probability that we get either one ev
over again under the same conditions .
Probability =
between 0 and 1 .
ex ) Pr that a person has blood type 0 =
Pr of e
↓
never atways
PREA ] :
probability of event A. Addition Rule : If 2 events are mutually exclusi
•
random that :
process that has two or more possible outcomes whose occurrence cannot the sum Of probabilities of each separately .
be prldlcted WI certainty .
Pr [ 0
-
or Ot ] = 0.374 t 0-066 =
0.440
'
ex ) flipping a coin , rolling a pair Of dice to see their sum . Pressing Shuffle
'
0h MUSIC .
biological :
randomly sampling 10 babies to see If female ( 1/2 ) Probabilities Of all possible mutually exclusive outcom
event of Interest :
any potential subset of all Possible Outcomes Of a random that ex ) blood type 8 outcomes
• .
=
" ' "
ex ) rolling a cue : result Is an even # ! result IS four " Pr [ Ot or 0
-
or At or A- or Bt or B- Or ABT or AB
•
possible outcomes : all outcomes In a trial .
•
Pr [ not A ] =
I -
Pr [ A ]
"
"
ex ) rolling a die : numbers I -6
General Addition Rule
5. 2 VENN DIAGRAMS • If events are not mutually exclusive : person to
•
probability of an event Is proportional to the area It Occupies In the diagram . Pr [ A ORB ] =
Pr EA ] t Pr [ B ] -
Pr [ A and B ]
M r = 0 If
/
-
Prca etting > 2) : 416=213 -
calculates probability that either A Or B ( or both
/
-
/ : .
If Pr [ A and B ] not subt
5. 3 MUTUALLY EXCLUSIVE EVENTS
•
two events that cannot both occur at the same time .
Pr [ A and B] = 0 5.6 INDEPENDENCE & MULTIPLICATION RULE
' '
independent If the occurrence of
'
ex ) events one and SIX
'
bc One die cannot produce both two events are
mutually exclusive
•
are .
probability that the other will also occur . ex ) roll
5. 4 PROBABILITY DISTRIBUTIONS •
If occurrence of one event provides at least som
•
describes the probability of each of the possible mutually exclusive outcomes of a random that . two events are dependent
Discrete Probability Distribution Multiplication Rule
-
for categorical and discrete numerical variables •
for independent events ,
Pr that they both occur
-
equally probable outcomes ( G- = 0.167 ) Pr [ A and B ] = Pr [ A] .
Pr [B ]
sum of all probability 1 ( probability of some OUTCOME OCCUR ) f- f- ¥
" "
3]
=
ex ) Pr [ 1st roll is 3 and 2nd roll
=
-
. IS = ✗
Continuous Probability Distributions
•
continuous numerical variables can take on any real # Value within some range .
•
height Of curve : probability density Independence Of More than TWO Events
•
can describe probability of any range of Values for Y .
ex ) Chance Of Offspring being green = 314 . Chanc
•
height of cont .
probability curve does NOT give the probability what IS the chance of all 10 Offspring s being gree
