Proof for Multiplication Rule of Probabilities

Why do we multiply probabilities when independent events occur after each other? This video shows the mathematical proof behind this rule.

[cbt]

I looked all over the place for an explanation on why we multiply. You made it really easy to understand. Thank you!!

[TheTamorres]

FINALLY I UNDERSTOOD WHY WE MULTIPLY!
NOTHING LIKE THIS ONLINE
THANK YOU

[exhalerwolf]

finally, a video that doesn't just state the rule and end the video. Great work.

[anthonyvillarama]

Thank you very much. The best explanation there is in youtube.

[srividyapratha]

Thank you so much for this, answered my questions.

[calummascarenhas]

Super, thank you! Just what I was looking for.

[sarahmedouni]

I would study math more often if my teacher had this voice

[sarthaksumanvishwakarma]

Say if we look at a case that We toss a coin and if heads comes we toss it again. But if we get tails we roll a dice then are probablity of HT, HH, T1, T2, T2, T3, T4, T5, T6 same?
In my book it is T1, T2, T3, T4, T5, T6 have probablity 1/2 x 1/6 = 1/12
while HT, HH have probablity 1/2 x 1/2 =1/4
That goes out of my intuation could u help??

[sohailsattani]

Thanks.. This really help me to understand the topic..
Can u pls solve below question:

A study by Peter D. Hart Research Associates for the Nasdaq Stock Market revealed that 43% of all American adults are stockholders. In addition, the study determined that 75% of all American adult stockholders have some college education. Suppose 38% of all American adults have some college education. An American adult is randomly selected.

a. What is the probability that the adult does not own stock?
b. What is the probability that the adult owns stock and has some college education?
c. What is the probability that the adult owns stock or has some college education?
d. What is the probability that the adult has neither some college education nor owns stock?
e. What is the probability that the adult does not own stock or has no college education?
f. What is the probability that the adult has some college education and owns no stock?

[Salgandarin]

Great vid!! Nothing as clear as this online.

[presidentworld]

The problem with this approach is its generality. It does not fully prove every case. In other words, it is not rigorous.