# TSI Math: Calculating Conditional Probability with Baye's Theorem

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Toni ordered pizza for a party, and needs it to arrive by 7pm. There is a 30% chance the pizza will be delivered late. If the pizza is late, there is an 80% chance it will be cold. Regardless of whether the pizza shows up on time, there is also a 31% chance it will be cold. If the pizza was cold on arrival, what is the probability it was delivered late?

Data Analysis, Statistics, and Probability | Probabilistic Reasoning |

Mathematics and Statistics Assessment | Probabilistic Reasoning |

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TSI | Mathematics and Statistics Assessment TSI Math TSI Mathematics |

TSI Math | Data Analysis, Statistics, and Probability |

TSI Mathematics | Data Analysis, Statistics, and Probability |

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### Transcript

will be cold regardless of whether the pizza shows up

on time There's also a thirty one percent chance it

will be cold if the pizza was cold on arrival

Well what is the probability It was delivered late Okay

well when we need to travel back in time to

answer a probability question our choices are the tricked out

delorean time machine or based there Um well since we

let out the delorean will go with based their amir

based serum comes in two versions and each one is

useful in different situations Take a look at the information

given by the question and put it in symbolic form

to figure out which version of bays to use Well

we want to know the probability that that pizza dude

was late given that the pizza was cold If we

set event b to be late delivery and a to

be cold pizza we're looking to find probability of be

given a probability that the pizza's cold given that it

was delivered late His point eight That means well this

p a given b thing is point eight Right That's

probability The probability of a late delivery is point three

or ah this thing the probability that pizza arrives cold

is point three one or ah this equation right there

Well the three things we do know and the one

thing we want to know match the simpler form Of

based serum which is this thing and we just plug

it all in and see if it works So we've

got point eight times point three over point three one

that's point two four point three one what does that

give us About a seventy seven and a half percent

chance that the pizza dude was late If the pizza

arrived cold gross and all congealed congealed What happened Your

pineapple pizza We need more pineapple on it Come on 00:01:50.688 --> [endTime] guys