# TSI Math: Predicting a Sequence of Probabilities

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?

Data Analysis, Statistics, and Probability | Probabilistic Reasoning |

Mathematics and Statistics Assessment | Probabilistic Reasoning |

Product Type | TSI |

TSI | Mathematics and Statistics Assessment TSI Math TSI Mathematics |

TSI Math | Data Analysis, Statistics, and Probability |

TSI Mathematics | Data Analysis, Statistics, and Probability |

Test Prep | TSI |

### Transcript

drawing two cards of the same suit in a row

Think of these problems with probability in cards as a

simpler form of poker Before we draw the first card

there are a total of four times thirteen or fifty

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

same suit is until after we draw the first card

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

The first card makes no contribution to the probability Suppose

first card we draw is a heart Well it could

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

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

we hard hearts Well we took a heart out of

the deck So now there are only twelve hearts left

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

fifty one cards in the whole deck The probability that

our second card is a heart that is twelve over

fifty one or twenty four percent not twenty five And

this is huge is a huge concept You have to

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

almost promise you this concept but as you take away

cards your probabilities change All right Because the first card

could be anything while the probability of randomly drawing two

cards of the same suit in a row is twenty

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

to consider each suit separately For example the probability of

randomly drawing two hearts in a row is thirteen over

fifty two times twelve over fifty one Well this probability

is the same Each of the other three suits we

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

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

each suit and you get this mess of a thing

here thirteen or fit to tone The this thing right

there four times that quantity because thirteen over fifty two

equals twelve over fifty one is point two for justice

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

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