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### Course: Math for fun and glory > Unit 5

Lesson 2: Random sampling warmup# Random sampling intuition

Created by Brit Cruise.

## Want to join the conversation?

- At0:47Sal said it could be one of those "one in a quadrillion chances that it picked white every time." There had been about 800 trial picks at that time. Is the odds of 800 white in a row really one in a quadrillion, or close to it?(22 votes)
- If the ratio of white to black beads is 2 : 1, then the probability of picking 800 white beads in a row is (2/3)^800, which is about 1.4 * 10^-141. This is one in ~7.5 * 10^140, which is 75 followed by 139 zeros. Which is way, way bigger than a quadrillion (1,000,000,000,000,000 - so has 15 zeros). It's about to 75 thousand quadrillion, quadrillion, quadrillion, quadrillion, quadrillion, quadrillion, quadrillion, quadrillion, quadrillion.(44 votes)

- Why does a realistic result approach a theoretical result from a top? it actually takes quite some time to go under 67%. Any ideas?(2 votes)
- why dont you just count the marblse ?(2 votes)
- You won't necessarily have the opportunity to see the marbles in the bag/cup/box/etc.

If you were to change the number of black & white marbles, and then cover up the left-hand side of the screen from a friend, you could have them guess how many of each color you put in.(3 votes)

- What is the website for that simulation(1 vote)
- It's right here on Khan Academy... just click to the next section on the navigation bar on the left (to "Weak law of large numbers") and you'll get to the simulation.

Here's a direct link, also:

https://www.khanacademy.org/math/recreational-math/math-warmup/random-sample-warmup/p/weak-law-of-large-numbers(3 votes)

- ye sit is larger and the moon is smaller(1 vote)
- the probability of it being a significant departure(1 vote)
- what does intuition even mean?(1 vote)
- According to my psychology textbook, intuition is an effortless, automatic feeling or thought.(1 vote)

- At0:20, Sal says that the percentage is getting pretty close to the actual ratio. At the time, it is at about 70%. Is that considered "close" to 50% in statistics? If not, why does he describe it that way?

EDIT: Just realized that 1:1 would be 50%. Would 4:2 be 66.6% or does 70% work too?(1 vote) - The bottom of the cup shows 66.7% that white will be picked. Still, the percentage keeps changing. I know it is random, but it should stay within 1-2% of 66.7, but sometimes it drifts to 70%. If the pattern continued, it would forever be random, but it should stay within that 66.7% range. I don't totally know why it drifts that far off the percentage average, but why should it?(1 vote)
- It is at 70% early on. Later, though, it definitely gets closer to 67%. The fewer we have picked, the easier some unlikely string is able to increase the percentage to 70%.(1 vote)

- This is a little off topic, but what program does he use for that?(1 vote)

## Video transcript

Voiceover:I have a little
simulation here that saves us time. It does the random picking for us. Voiceover:Mm-hmm. Voiceover:And it allows me
to start with four whites and two blacks, and I'm
going to have the computer do many selections for us. Voiceover:So, this is every
selection the computer's doing, the equivalent of randomly
picking out a marble. It's shaking it and randomly
picking it, and you see that now the percentage of
white, it's getting pretty close to the actual percentage, or
a 4:2 ratio, I should say, of white to black. Voiceover:So, I think I
believe you now, because at the beginning, I see a lot of variation- Voiceover:Right. Voiceover:On this graph
over time, and now it's kind of flat-lining. Voiceover:It's definitely, it
feels like it's converging to the actual proportion, and once again, there's some chance that it didn't. We could have, it could
have been just one of those one in a quadrillion circumstances
(laughs) where you just kept picking a white every
time, but this is consistent with the intuition, as
the more trials you have, it just becomes harder and harder, the probability of it being a
significant departure from the actual proportion becomes lower.