2. The probability of being dealt a pair in apoker hand (ranks aabcd where a != b !=c != d) is:

a

!

131

"!

123

"!

42

"!

41

"!

41

"

/

!

525

"

b

!

132

"!

122

"!

43

"!

41

"!

41

"

/

!

525

"

c

!

131

"!

123

"!

42

"!

41

"!

41

"!

41

"

/

!

525

"

d none of the above

2

State 134 Lec 8

Warmup 1 00 1 10

Answ 7 CX'T EdB 3 EXTINCT

aabcdt aabdc aacbd aacdb9acbd

aacdbaabtb.ba

Announcement Wednesday's Q2 Logistics will be released soon

ias ne interpretation of Enumber of arrangements of

two Is in 5 slots

5 hypergeometric distribution

Suppose a population d size N contains

G good and 13bad elements Cw GtBA Sammie size n with g good and b badelements neg b is chosen at randomu replacement IPC 9goodand bbad 8 3

9Parameters N Population size

G Goodin populationn sample size

Abreu HG N G n

E P Pokerhandis 4 of a kind rank aaaa b atbN number of cards 52G number ok rank a card indeck 4n sample size 5

not a ba

7 liking MGRr cchoose n

1 rankforgamesA Poker mot i3 since aaaa b f bbbba

today n

reviewstudentconcepttest responsesSec 2.5 more hypergeometricSec 25 CountingstrategySec 2.5 Binomial approt to hypergeometric

w

or

8 card poke hand

nd Chance ge itnjaaabbbcd

I CNN.tk'D

t

puaettcehyyevgeouo.tvyou airela friend are playing poker If each of you

are dealt 5 Cards from the same deck what is thechance that you both get a 4 of a kid Cranks aaaaq

b

P friend and you get 4 of kind

P friend 4 kind P you 4 kind friend 4Katsd

couwtdnyst.ru tegyiTry and break the problem into a sequence

of steps and apply the multiplication rule Above we

find the chance your friend gets 4 of a kind andthe probability you get 4 ota kind given that yourfriend got 4 of a kind

EI There are 3 Democrats 2 Republicans and2 Independents sittingaround a table Whatis the chance the Dem sit together theRep sit together and the Ind sit together

we break up the Problems

Dem Rep together Inder togethertogether given Demtogether sheer D and R

I together

c D e lD R R R R

7 I 21

n I

I ifor IH D 2 positions

for it Rso next

to D

Note If R.R are sitting on a

bench instead of around a table the airs we

would be

EXE

In a well shuffled deck find the probabilitythat J Q K appear as 12 consecutive cards andthe T are grouped together Q are grouped togetherand K are groupedtogether

JJJJQQQQKKKKorQQQQJJJJKKK.IS etc

We can break the problem into partsFirst find the chance that JJJJQQQQkKkKis the first ie cards out of 52 in r't't orderthis is

Then 3 is all ways you can get9,44,407

different orderings JJ JJ QQQQ and K KKKin the 1st 12 cards

Imagine the 12 cards are glued togetheras one fat card so our deck now has

41 cards There are 41 position's for the

fat card Hence the answer is

i