[Discrete Mathematics] Conditional Probability
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- เผยแพร่เมื่อ 15 มี.ค. 2015
- 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.
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![[Discrete Mathematics] Axioms of Probability](http://i.ytimg.com/vi/xuv6BCR-iNc/mqdefault.jpg)
19:32 Do u mean dependent?
surely at 19:40 you meant dependent.
Just want to be sure
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.
Yeah that tripped me up too
Thank you very much, I had some trouble with this topic but your video gave me a better understanding.
Thank u very much..so helpful! You are great
Very informative videos , please make some on conic sections. It will be a lot helpful.
man you are carrying me thru uni, thanks
Thankyou so much for this ❤️
so helpful!
+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?
thanks, TheTrev
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
That video is fantastic, & I would like to shake your hand.
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?
Thank you, you saved my degree
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'
If B went beyond the perimeter of A, you simply swap them in the formula.
Just died laughing at your joke at 7:57
At 19:35, how did you get 1/9 for P(A n B)?
Cheers!
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.
hey why is it P(B|V) instead of P(V|B) for vegetarians that like broccoli?
Hi Treva. if P(A' U B') = 1- P(AUB), what will be P(A' n B')?
Just replace the intersection symbol by the union symbol.
i cant do this as much as i try, i have been taught many times and i just cant do it
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.
you just said that both cases are independent
Confused at 15:10
Is the answer 1/12 or 1/6? The independent part confused me.
The real answer is 1/6. This just goes to show that the other formula doesn't work for dependent events.
@@axhraf7712 Thank you so much for replying to my two questions. Much appreciated!
Trevor, thanks for the wealth of videos. I am now wealthier than Bill Gates knowledge-wise, and slowly ascending the ranks to Jeff Bezos.
Trev you are my God.
i don't understand T T
i'm a bit confused
at 10:12 shouldn't it have been P(B | V) ?
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)
@@axhraf7712 ahh thanks a lot
Vegetarian *TRIGGERED*
Meat Eaters