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Probability 101

2010-11-09 · Hank · watch on YouTube · Science & nature · explainer learning

Hank teaches basic probability as the art of putting meaningful numbers on random events: favourable over possible outcomes, complements, multiplying for AND and adding for OR, then applies 'go for ANDs, avoid ORs' to absurd life-or-death word problems.

What is said

00:00:00 — Hook: everyone flips a coin ten times; Hank 'knows' what happened overall, about 100 in 102,400 flipped ten heads; nothing special about your coin

  • ★★ Hank asks John and everyone watching to pause the video, get a coin and flip it ten times. — 00:00:00
  • ★★★ Hank says each flip is random and he can't know any one viewer's coin, but he knows what happened overall, not by being psychic but because he knows about probability. — 00:00:08
  • ★★ Hank tells viewers who flipped ten heads that there is nothing special about their coin, or about them, so it is no magical coin to bet on in Vegas. (playful) — 00:00:48
  • ★★★ Hank says the odds of ten heads in a row are 1 in 1024, so if 102,400 people flipped ten times, roughly 100 got ten heads and 100 got ten tails. — 00:00:55

00:01:12 — Probability basics: definition, P(A) as favourable over possible outcomes, coins, AND as multiplication, dice and complements, poker hands, the 0-1 scale, OR as addition

  • ★★★ Hank defines probability as the science, or art, of assigning meaningful numbers to things no one can really know, allowing real, measurable conclusions about random events. — 00:01:12 > «the ART of assigning meaningful numbers to things that no one can actually really know»
  • ★★★ Hank says a single random event is unpredictable, but when it happens many times, patterns become obvious and unavoidable. — 00:01:26
  • ★★★ Hank defines P(A): when all outcomes are equally likely, it is the number of events where A is true divided by the total number of events. — 00:01:35
  • ★ Hank says no one, not Miss Cleo, Albert Einstein or even Dr. Manhattan, could know where an individual coin would fall. (playful) — 00:01:52
  • ★★ Hank says a coin has a 1 in 2 (50%) chance of heads, so of 100 flipped coins roughly 50 land heads, with some variation. — 00:02:05
  • ★★★ Hank says the chance of A and B is the product: two heads is 1/2 times 1/2, or 1/4, and ten heads is (1/2)^10, or 1/1024. — 00:02:25
  • ★★★ Hank says the chance of rolling a 5 on a die is 1/6, and its complement, 1 minus P(A), gives 5/6 for not rolling a 5, an important idea; an even number is 3/6, or 1/2. — 00:03:05
  • ★★ Hank says there are 2,598,960 possible poker hands and 123,552 two-pair hands, so the chance of two pair is 4.7%; he looked the counts up on the internet. — 00:03:57
  • ★★ Hank says probabilities fall on a scale from zero (impossible) to one (certain), which is why they are often given as percentages, i.e. out of a hundred. — 00:04:23
  • ★★★ Hank says multiplying P(A) by P(B) works only when A does not depend on B, giving snake eyes 1/36, while 'A or B' adds them: a 2 or a 3 on a die is 1/3. — 00:04:44

00:05:19 — Three absurd life-or-death word problems (cigarettes and piranhas, ninja poison dart and mixed pills, terrorist velociraptor) solved with 'go for ANDs, avoid ORs'

  • ★ Hank says he hated word problems in school, but now that he is teaching them he loves them. (playful) — 00:05:30
  • ★★ In his first made-up word problem (1-in-5 terrorist risk per cigarette, 40% piranha risk per premarital sex), Hank computes survival as 80% times 60%, 48%. (hypothetical) — 00:05:39
  • ★★★ Hank's tip: always go for ANDs and avoid ORs, turning 'the chance of dying' into 'surviving both risks' with the 1 minus P(A) trick. — 00:05:59 > «always go for "ANDs" and avoid "ORs."»
  • ★★ In the poison-dart problem (6 Tylenol, 4 Imodium AD, 4 antidote pills, three picks), Hank gets a 33% chance of no antidote, so 67% survival. (hypothetical) — 00:06:28
  • ★★ In the terrorist-velociraptor problem (one bullet, four trigger pulls, 30% chance a hit stops it), Hank gets 32% for no shot, 68% for firing and 20% survival. (hypothetical) — 00:07:38
    • number check: 32% — doubtful
    • number check: 68% — doubtful

00:08:27 — Sign-off: John will educate Hank more on Wednesday

  • ★★ Hank says he looks forward to John educating him more on Wednesday. — 00:08:29

Humor (significant)

  • Hank claims he knows what happened to everyone's coins because he is psychic, because he is omniscient... — 00:00:22 > «Because I have a little camera installed in all of your rooms and I WATCH YOU AS YOU WATCH ME.»
  • Viewers who flipped ten heads think they have a magical coin to take to Vegas. — 00:00:49 > «there's nothing special about your coin and there's nothing special about you.»
  • Hank hated word problems in school; they made him want to kill himself. — 00:05:35 > «But now I'm teaching them so I frakkin' love 'em.»
  • First word problem: every cigarette carries a one-in-five chance of being killed by a terrorist. — 00:05:43 > «you have a 40% chance of being devoured by a tank of venomous piranhas.»
  • For those who thought they'd avoid the pill problem by drinking the whole bottle: you died of antidote overdose. — 00:07:07 > «You're DEAD and YOU CAN'T CHEAT YOUR WAY OUT OF WORD PROBLEMS.»
  • Final word problem: you have a gun with one bullet in an unknown chamber. — 00:07:45 > «You're being attacked by a terrorist velociraptor.»

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