How do you solve conditional probability examples?

How do you solve conditional probability examples?
What is the probability of an event A given that event B has occurred?
This is conditional probability, solved by the formula that P(A|B) which reads "probability of A given B" is equal to the P(A intersect B)/P(B).
Three examples are examined.

Conditional Probability Formula: P(A|B) = P(A and B)/P(B)

[kennethhowell]

I have an IQ of 1. But because of your ability to teach anyone Bayes theorem it is starting to make sense. You are the best. Thank you!

[NK-mnzu]

Maths teacher from Blighty here! 👋🏽 My students prefer the Venn diagram method. 😊

[amanda-clairebennett]

Thank you, it was very helpful, really appreciate it. Your content is great. From Perth WA.

[Fret-knot]

Beer, whisky, wine, rum.... In fact, the lot. 100% probability of being drunk, at least twice a week.

[pcrkqsx]

I love these videos the jump where you immediately discount the 70 throws me. I wonder is there is a platform to do more of these questions to become more familiar with the process?

[afarbasquiat]

Thanks for this amazing video, cat people are also awesome !!!!

[drawforge]

Ah this makes me remember many many imo sums involving P and Cs

[Cpt_Dave]

Oh, misunderstood the second one. Thought 40 people drink beer, 30 whiskey and 20 drink both, meaning a total of 90 people drink alcohol.
But you mean that out of the 40 people who drink beer, 20 also drink whiskey.

Otherwise it would have been 1/3.

[retu]

I don't get the beer and whiskey question. "What is the probability of a person drinking beer, if chosen from this group of 120 people" would be 50 %, wouldn't it? But the question states "If the person drinks beer", so that one is a certain. Then it's asked: "What is the probability that the person drinking beer also drinks whiskey?". Wouldn't the answer to that be 20/60 = 33, 33%? Cause there are 60 people who drink beer, but only 20 of those also drink whiskey? Shouldn't the diagram be: beer = 60, both = 20, whiskey = 50? So 40 that drink only beer, 20 drink both, and 30 that drink only whiskey.

I guess the wording just doesn't make sense to me, since i'm not a native speaker.

*Edit* The next question has the same problem i think. If it's certain the person chosen has a dog for example, then the probability of having both is 5/45, no? Would be way less confusing it the question was: "Out of 70 people 40 have dogs, 15 have cats, 5 have both and 15 have no pets". Then you would get the expression that the 5 who have both have to be included in the 40 and 15.

[orac]

The probability of me solving any conditional probability equations is ZERO

[mdcs]

Sorrry. Got to tell you. I'm at 2:20 and I understand EVERYTHING so far. I'm a frickin' genius!

[samburdge]

I'd drink though I don't drink as often as I used is it 40, 15, 5 equal 50 of that being 40 people own dog, 15 own cat, 5 both equaling 60 people