Post on 21-Sep-2020
transcript
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
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8 card poke hand
nd Chance ge itnjaaabbbcd
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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