Math-> Probability

Recall

PropI NEUF P E PCA PLEA

F

her PropI PC.EU FUG PCE tpCF tPCG REF PCFG REG PCEFG

E F Info

G

E A school has 100 students and 3 Language courses S F G

28 students are taking S 26 F

14 G 12 Stf 4 St G 6 ft G 2 K S Ft G

a If a student is selected at random what is prob the student takes non language class

S F

6 G

b If a student is selected at random what is prob student

takes only Spanish 14

c If a student is selected at random what is prob student takes exactly 2 Language classes

1ot o4

d If a student is selected at random what is the prob that student takes at least Language classes

10 2 4 2

er 1 5 1446 1 0 v w O L I L

2.3 conditional probability

MotivatingEI Roll 2 dice a Prob we roll a sum of H

b Given that the first dc lands on 6 what is the conditional prob we roll a sum of II

y second die needs to land on 5

G Given that the first die lands on 1 what is the Conditional prob we roll a sum of II

OB Pitta IA cEi

PCB

Def suppose F is an event w prob PCF 0 Then the conditional proI thatEoaursg.ve that

FoecusisPCElFPCEf ptr

Prob of F given f

Re arranging above gives PCErtPCEIAPCFS.LT SETI east

In previous Ex

let E roll a sum of Il I I die lands on G E I die lands on I

b MEI E PfEI i PCE F PC sum of 11 and I died 6

1 36 pain 6,5

c REI E PCpE

E A coin is flipped twice What is the prob that both flaps are T given that

a first flip is T

Let B both flip are T F II flip is T

PIBIES Pcf

b at least one flip is T

Let A at least one flip is T

PCBtA PCpAB

Uniform sis 5 E CHHI CHI 151 4 IIA CIT

Fact If S is a uniform ss and E and F are events in S we may evaluate PCEIF by treating the outcomes in F as the new niformDs.s

This called the reduced sis

In the preu Ex lb A HiT IIHS IT T IAK 3

PCBIA

Rectal PCEF PCElf pCF

Multiplicative PCE.EE Ea PCE PCE.IE PCEzlEEd

PCEn1EEa Eat