Conditional Probability and Bayes' Theorem

Main post link -> https://brilliant.org/assessment/techniques-trainer/conditional-probability-and-bayes-theorem/

This week, we are very happy to have a guest post by Matt Enlow on Conditional Probability And Bayes' Theorem.

You may first choose to read an introduction to Probability.

#Combinatorics #KeyTechniques

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Math	Appears as
Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

Comments

Kudos to Matt! This is very well written!

Bob Krueger - 7 years, 11 months ago

Agreed. I was very excited when I received the writeup, and we prepared the rent posts on expected value and variance to get students used to these probability concepts, before blowing your mind with Bayes' Theorem.

Calvin Lin Staff - 7 years, 11 months ago

Mind-blowing indeed.

Justin Wong - 7 years, 11 months ago

Thanks to Bob for the kudos, and to Calvin for the opportunity! I really enjoyed putting it together.

Matt Enlow - 7 years, 11 months ago

There's no way to see the solutions to the practice problems, right? Because I'd love to check my answers.

Tim Vermeulen - 7 years, 11 months ago

As of right now, no, but I'm sure you're not the only one that would like to check your answers! I'll talk with Calvin to see what the best way to go about that would be. Thanks for the suggestion!

Matt Enlow - 7 years, 11 months ago

are you people aware that probability type questions can easily be confronted with programing...like for example in Java...the java.util.Random class if coded properly can easily estimate up to a great accuracy the probability of an event

Rajarshi Banerjee - 7 years, 11 months ago

Simulations can be an effective way of estimating probabilities, but that takes all the fun math out of it.

Bob Krueger - 7 years, 11 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$