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TSI Math: Predicting a Sequence of Probabilities 55 Views


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Description:

A standard deck of playing cards contains 4 different suits, each of which has 13 cards. Assuming the deck is shuffled, what is the probability of randomly drawing 2 cards of the same suit in a row?


Transcript

00:02

Okay sy mash members get a whole new section on

00:04

probability or probabilistic reasoning So let's dive in here to

00:08

a deck of cards A standard deck playing cards contains

00:11

four different suits each of which has thirteen cards Assuming

00:14

the deck is shuffled what is the probability of randomly

00:17

drawing two cards of the same suit in a row

00:24

Think of these problems with probability in cards as a

00:28

simpler form of poker Before we draw the first card

00:31

there are a total of four times thirteen or fifty

00:33

two cards in the deck We don't know what the

00:36

same suit is until after we draw the first card

00:39

so it doesn't matter what the first card is right

00:41

The first card makes no contribution to the probability Suppose

00:44

first card we draw is a heart Well it could

00:47

be any suit but we'll use hearts Is an example

00:49

here because we're naturally loving people Hear it Some upright

00:52

we hard hearts Well we took a heart out of

00:54

the deck So now there are only twelve hearts left

00:58

in the deck right One goes away and there's only

01:01

fifty one cards in the whole deck The probability that

01:04

our second card is a heart that is twelve over

01:07

fifty one or twenty four percent not twenty five And

01:10

this is huge is a huge concept You have to

01:13

know this because it'll be on the test We can

01:15

almost promise you this concept but as you take away

01:17

cards your probabilities change All right Because the first card

01:21

could be anything while the probability of randomly drawing two

01:24

cards of the same suit in a row is twenty

01:26

four percent Another way to arrive at same answer it's

01:29

to consider each suit separately For example the probability of

01:32

randomly drawing two hearts in a row is thirteen over

01:35

fifty two times twelve over fifty one Well this probability

01:39

is the same Each of the other three suits we

01:42

don't care which suit the cards are as long as

01:44

it's the same So add up the individual probabilities for

01:48

each suit and you get this mess of a thing

01:50

here thirteen or fit to tone The this thing right

01:53

there four times that quantity because thirteen over fifty two

01:58

equals twelve over fifty one is point two for justice

02:02

before it's kind of like we did a little proof

02:03

there anyway right answer gets d it's twenty four percent 00:02:07.44 --> [endTime] Them's The odds

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