Conditional probability and independence | Probability | AP Statistics | Khan Academy

Use conditional probability to see if events are independent or not.

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[gachaluna]

Khan Acddemy videos are always helpful for me when I have trouble in math. :)

[nsuinteger-au]

best explanation i've found for conditional independence with a real life example. cheers!

[filmonokbu]

Hi! Do you have a playlist of lectures on probability and statistics?

[TasyaAdzkiya]

Is it true that the reason of the probability of the events that are delayed given it's snowy is 12/20 and not 12/35 is that we interpret it as, "How many delayed events there are in all of snowy events per total of snowy events?"

If it were the other way around, which is the probability of events that are snowy given that it's delayed, it's going to be 12/35 because it's the same as asking, "How many snowy events there are in all of delayed events per total of delayed events?"

Also, the reason why both of them has to be equal (or at least similar) in order to be independent is that if it were independent, the probability of (in this case) delayed events is not dependent on the snowy events, so it doesn't matter what happens to the snowy events, it won't affect the probability of the delayed events. So, the probability of delayed events and the probability of delayed events given that it's snowy is equal or similar (again, because the delayed events doesn't depend on the snowy events, so it won't change anything).

I also think the reason why Sal said it has to be equal or AT LEAST SIMILAR is because when we are dealing with experimental probability, any random chance can happen and skew the result, and it won't be perfect like theoretical probability.

So, is my summary true? Please let me know if I'm right or wrong. Thanks in advance.

[tawseeftaher]

can we get it by calculating

P(delayed), P(snowy), p(delayed and snowy)

if
p(delayed and snowy) = p(delayed) * p(snowy)
then it's independent.

in this case, it's not.
since 12/365 isn't equal to 35/365 * 20/365 .

[The-cyber-imbiber]

To truly know if they are intendent or not, wouldn't you need to do a hypothesis test? If so, which test would be used?

[vvsiva]

I think the other way --> P(delayed) and P(delayed|not snowy) --> these two are independent