Probability solution: A Total of n balls, number of 1 through n... <br /><br />Interesting Probability question<br /><br /><br />more video lists:<br />################<br /><br />Probability and discrete mathematics:<br /><br />######################################################################<br /><br />Probability interview questions:<br /><br /><a href="https://www.youtube.com/watch?v=qphhG_1rWf8&list=PLg9w7tItBlZtI1eM6znSYfyDEaqQtUx5b" target="_blank" rel="nofollow">https://www.youtube.com/watch?v=qphhG_1rWf8&list=PLg9w7tItBlZtI1eM6znSYfyDEaqQtUx5b</a><br /><br /><br /><br />Probability theory:<br /><br /><a href="https://www.youtube.com/watch?v=8s-nyRLBsDo&list=PLg9w7tItBlZsvciKHBx8lXXnCtQ7Ou4cV" target="_blank" rel="nofollow">https://www.youtube.com/watch?v=8s-nyRLBsDo&list=PLg9w7tItBlZsvciKHBx8lXXnCtQ7Ou4cV</a><br /><br /><br />Complex analysis:<br /><br /><a href="https://www.youtube.com/playlist?list=PLg9w7tItBlZsYfYG6dUISItqsSRSXaX4B" target="_blank" rel="nofollow">https://www.youtube.com/playlist?list=PLg9w7tItBlZsYfYG6dUISItqsSRSXaX4B</a><br /><br />Combinatorics:<br /><br /><a href="https://www.youtube.com/playlist?list=PLg9w7tItBlZvQt0YNfCqcULzrPme2ai7K" target="_blank" rel="nofollow">https://www.youtube.com/playlist?list=PLg9w7tItBlZvQt0YNfCqcULzrPme2ai7K</a><br /><br /><br />additive combinatorics:<br /><br /><a href="https://www.youtube.com/playlist?list=PLg9w7tItBlZseUrmXgf_2yc2NI_obVUhB" target="_blank" rel="nofollow">https://www.youtube.com/playlist?list=PLg9w7tItBlZseUrmXgf_2yc2NI_obVUhB</a><br /><br />微積分 高等微積分 代數<br /><br />Calculus and advanced mathematics (abstract algebra):<br /><br />######################################################################<br /><br />Real analysis<br /><br /><a href="https://www.youtube.com/playlist?list=PLg9w7tItBlZumEJ4DacAKgstCvDHKtY63" target="_blank" rel="nofollow">https://www.youtube.com/playlist?list=PLg9w7tItBlZumEJ4DacAKgstCvDHKtY63</a><br /><br /><br /><br />Reduction formula in Calculus:<br /><br /><a href="https://www.youtube.com/playlist?list=PLg9w7tItBlZubmhgkHoHvje1uOASnkcke" target="_blank" rel="nofollow">https://www.youtube.com/playlist?list=PLg9w7tItBlZubmhgkHoHvje1uOASnkcke</a><br /><br /><br /><br />Integrals of trigonometric functions:<br /><br /><a href="https://www.youtube.com/playlist?list=PLg9w7tItBlZuwEER2YvFV06ri6i1Cj3hh" target="_blank" rel="nofollow">https://www.youtube.com/playlist?list=PLg9w7tItBlZuwEER2YvFV06ri6i1Cj3hh</a><br /><br /><br /><br />(algebraic geometry)代數幾何筆記<br /><br /><a href="https://www.youtube.com/playlist?list=PLg9w7tItBlZssQ4Smzgp_bk2rEszKaW0B" target="_blank" rel="nofollow">https://www.youtube.com/playlist?list=PLg9w7tItBlZssQ4Smzgp_bk2rEszKaW0B</a><br /><br /><br /><br />Linear algebra Proof:<br /><br /><a href="https://www.youtube.com/playlist?list=PLg9w7tItBlZueH6LMeYzzwPMUlIaRhCZo" target="_blank" rel="nofollow">https://www.youtube.com/playlist?list=PLg9w7tItBlZueH6LMeYzzwPMUlIaRhCZo</a><br /><br /><br /><br />環論(ring theory):<br /><br /><a href="https://www.youtube.com/playlist?list=PLg9w7tItBlZs9w4wrNAuv4oJdrt-sIWUP" target="_blank" rel="nofollow">https://www.youtube.com/playlist?list=PLg9w7tItBlZs9w4wrNAuv4oJdrt-sIWUP</a><br /><br /><br /><br />Abstract Algebra:<br /><a href="https://www.youtube.com/playlist?list=PLg9w7tItBlZsyZ0Ri0IDPYEwDxDXjCqB0" target="_blank" rel="nofollow">https://www.youtube.com/playlist?list=PLg9w7tItBlZsyZ0Ri0IDPYEwDxDXjCqB0</a><br /><br />Group theory (群論):<br /><a href="https://www.youtube.com/playlist?list=PLg9w7tItBlZu4Qkxz2WSk4eYZmDAC8ZY0" target="_blank" rel="nofollow">https://www.youtube.com/playlist?list=PLg9w7tItBlZu4Qkxz2WSk4eYZmDAC8ZY0</a><br /><br /><br />Galois theory:<br /><a href="https://www.youtube.com/playlist?list=PLg9w7tItBlZsepuNJ3tOnG238M03KrKaG" target="_blank" rel="nofollow">https://www.youtube.com/playlist?list=PLg9w7tItBlZsepuNJ3tOnG238M03KrKaG</a><br /><br /><br /><br />數論跟其他:<br /><br />number theory and others:<br /><br />###########<br /><br />Riemann Zeta functions:<br /><br /><a href="https://www.youtube.com/playlist?list=PLg9w7tItBlZu4ncqL53iPd1GmwKq8yYoM" target="_blank" rel="nofollow">https://www.youtube.com/playlist?list=PLg9w7tItBlZu4ncqL53iPd1GmwKq8yYoM</a><br /><br /><br /><br />Math related to pi:<br /><br /><a href="https://www.youtube.com/playlist?list=PLg9w7tItBlZuzFft3Y5h1LRaNvAv7ruKe" target="_blank" rel="nofollow">https://www.youtube.com/playlist?list=PLg9w7tItBlZuzFft3Y5h1LRaNvAv7ruKe</a><br /><br /><br /><br />Number theory:<br /><br /><a href="https://www.youtube.com/playlist?list=PLg9w7tItBlZvGgPYrFxfGWaQgQBrLOOws" target="_blank" rel="nofollow">https://www.youtube.com/playlist?list=PLg9w7tItBlZvGgPYrFxfGWaQgQBrLOOws</a><br /><br /><br /><br />Set Theory:<br /><br /><a href="https://www.youtube.com/playlist?list=PLg9w7tItBlZsDqBUL-CIHcVVBs9EODL_J" target="_blank" rel="nofollow">https://www.youtube.com/playlist?list=PLg9w7tItBlZsDqBUL-CIHcVVBs9EODL_J</a><br /><br /><br />High school math & AP calculus:<br /><a href="https://www.youtube.com/playlist?list=PLg9w7tItBlZv165XaBIyj03q3WSMMUqDo" target="_blank" rel="nofollow">https://www.youtube.com/playlist?list=PLg9w7tItBlZv165XaBIyj03q3WSMMUqDo</a><br /><br /><br />Solving polynomial equation:<br /><br /><a href="https://www.youtube.com/playlist?list=PLg9w7tItBlZsheN8dz8LLPy99AaLb7_-7" target="_blank" rel="nofollow">https://www.youtube.com/playlist?list=PLg9w7tItBlZsheN8dz8LLPy99AaLb7_-7</a><br />...<br /><a href="https://www.youtube.com/watch?v=vnl-z7OvMSo" target="_blank" rel="nofollow">https://www.youtube.com/watch?v=vnl-z7OvMSo</a>