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[Discrete Mathematics] Conditional Probability

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We talk about conditional probability.
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Today we look at Conditional Probability, showing the Law of Total Addition, the Multiplicative Law, and Bayes' Theorem. We'll then do an example with real life vegetarians and broccoli, where we put them head-to-head in an ancient Roman battle arena where they will fight to the death. I'm kidding, of course. Let's be real, nobody ever reads the description.
Hello, welcome to TheTrevTutor. I'm here to help you learn your college courses in an easy, efficient manner. If you like what you see, feel free to subscribe and follow me for updates. If you have any questions, leave them below. I try to answer as many questions as possible. If something isn't quite clear or needs more explanation, I can easily make additional videos to satisfy your need for knowledge and understanding.

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15 мар 2015

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Комментарии : 38

@tekluandargachew4303 2 года назад

19:32 Do u mean dependent?

@joshuauwaifo4037 9 лет назад

surely at 19:40 you meant dependent. Just want to be sure

@Trevtutor 9 лет назад

Joshua Uwaifo Yes, the first set of events in a loaded coin is dependent, not independent. Added an annotation. When you say independent, dependent, not independent, and not dependent a lot, you tend to get your words mixed up. I might redo this at some point.

@InfinantGamers 6 лет назад

Yeah that tripped me up too

@taiwooyekanmi7725 8 лет назад

Thank you very much, I had some trouble with this topic but your video gave me a better understanding.

@blertahasani1511 8 лет назад

Thank u very much..so helpful! You are great

@kallihale5197 Год назад

I think he mis-spoke at 19:21? It should be that they are dependent, because P(A intersect B) != P(A) * P(B) by the definition given at 12:54

@thinkingaboutjinchen3165 7 лет назад

Thankyou so much for this ❤️

@elitea6070 2 года назад

man you are carrying me thru uni, thanks

@smhemant9111 6 лет назад

Very informative videos , please make some on conic sections. It will be a lot helpful.

@karentan111 4 года назад

so helpful!

@johanronkko4494 7 лет назад

+TheTrevTutor So... Is it fair to say that when P(A intersection B) = P(A)P(B) we have independency and when P(A intersection B) != P(A)P(B) we have dependency?

@hieunguyenthang3535 4 года назад

thanks, TheTrev

@mohammadrezajavadi3498 9 месяцев назад

That video is fantastic, & I would like to shake your hand.

@aleksandarjankovski6542 Год назад

A quick question: the very first example was solved by dividing the cardinality of A and B by the cardinality of A; that is 2/10. Perfect. But then the conditional prob rule is P(A and B)/P(B). Should it not be that P(B|A) is the cardinality of A and B divided by the cardinality of A?

@stephaniewainaina4150 3 года назад

hey why is it P(B|V) instead of P(V|B) for vegetarians that like broccoli?

@markanthonyoccena7345 3 года назад

Thank you, you saved my degree

@mulimotola44 7 лет назад

6:20 this drawing only works when B is a subset of A_Union_A' right? If B went beyond the perimeter of A and A' then we'd see that B is more than its intersections with A and with A'

@anastasiagavrilita6567 4 года назад

If B went beyond the perimeter of A, you simply swap them in the formula.

@potatootter5088 2 года назад

At 19:35, how did you get 1/9 for P(A n B)? Cheers!

@axhraf7712 2 года назад

P(A intersection B) = the probability that the first one is a tail AND they are both the same. This only happens in one case, TT. For which the probability is 1/9. Why is that probability 1/9? -> Well you're rolling twice. The odds of the first die landing on tails is 1/3 (with these loaded dice). The odds of the second one landing on tails is again.. 1/3. so you get: 1/3 and 1/3 = 1/3 × 1/3 =1/9.

@slocombhouse5329 5 лет назад

Just died laughing at your joke at 7:57

@ndekinoah3101 Год назад

Hi Treva. if P(A' U B') = 1- P(AUB), what will be P(A' n B')?

@PMA_ReginaldBoscoG 6 месяцев назад

Just replace the intersection symbol by the union symbol.

@saketkumar4972 11 месяцев назад

you just said that both cases are independent

@potatootter5088 2 года назад

Confused at 15:10 Is the answer 1/12 or 1/6? The independent part confused me.

@axhraf7712 2 года назад

The real answer is 1/6. This just goes to show that the other formula doesn't work for dependent events.

@potatootter5088 2 года назад

@@axhraf7712 Thank you so much for replying to my two questions. Much appreciated!

@jesusalvarez4656 6 лет назад

i cant do this as much as i try, i have been taught many times and i just cant do it

@nadeemjq 5 лет назад

Great video! Here is a hail mary if you absolutely cannot remember the formula in the vegetarians vs broccoli example: Start thinking in frequencies, or absolute numbers. So, instead of vegetarians and meat-eaters making up 100% of the people, we say they total 100 people. Then, 25 people are vegetarian. And, of these, 80%, or 20 people are broccoli lovers. The remaining 75 people are all meat-eaters. And, of these 40%, or 30 people, are broccoli lovers. This means we have 20 broccoli lovers from vegetarians and 30 from meat-eaters, totalling 50 broccoli lovers. Of the 50 broccoli lovers, 20 are vegetarians. So, the probability is 20 / 50, or 40%. In my above method, I'm actually doing exactly what the formula does, but it's slightly easier to reason about. At least in this case.

@particleonazock2246 3 года назад

Trevor, thanks for the wealth of videos. I am now wealthier than Bill Gates knowledge-wise, and slowly ascending the ranks to Jeff Bezos.

@melaniemurday3138 3 года назад

i'm a bit confused at 10:12 shouldn't it have been P(B | V) ?

@axhraf7712 2 года назад

No, the question is what is the probability that they like broccoli, given that they're vegetarian. This is a good way to never get it confused: "What is the probability of event A happening knowing that event B happened?" -> P(A|B)

@melaniemurday3138 2 года назад

@@axhraf7712 ahh thanks a lot