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Course: Statistics and probability>Unit 6

Lesson 3: Sampling methods

Picking fairly

Sal determines if a few different methods of a magician choosing a volunteer are fair. Created by Sal Khan.

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• This may have been answered somewhere else, but how exactly does a random number generator work?
• This is a very complex and studied question.

True randomness is not achievable using mathematical methods, the best we humans can do is a pseudorandom number generator, in simple terms:
- you choose a seed (any number), most (pseudo)random number generators use the current time in seconds as the seed and then do some calculations with that value to output a (pseudo)random number.

There's more details in the Wikipedia article: http://en.wikipedia.org/wiki/Pseudorandom_number_generator
• Why not have the most obvious amount of pieces of paper 15, in the problem?
• Having 15 pieces of paper would indeed be more straightforward and would ensure that each child receives an equal number of pieces of paper, thus making the selection process fairer. It's unclear why the magician chose to use larger numbers of pieces of paper in the scenarios described in the problem.
(1 vote)
• Hi! I have a hard time solving for the percentage so i can find the weighted average. The phrase says: the final examination in a certain course counts three times as much as each of the three examinations. How will i interpret this?
• It's possible that there's a word missed out. If the sentence said "the final examination ... counts three times as much as each of the OTHER three examinations" then that would make sense -- there are four examinations, and the final one is worth three times as many marks as each of the first three. I think this is the most reasonable way to interpret the sentence. It doesn't make much sense as it is.
• Just saying too, the room could have 0 windows and then they're all S.O.L.
Just sayin'
• how do you make a time stamp for a video?
• Just write the minute and second separated by a colon.
(1 vote)
• The number of windows is random but not evenly distributed cause there is no info or guarantee that the house has the same windows in every room. Did I correctly understand? If yes why it is mandatory to evenly distributed?
(1 vote)
• Yes, you understood correctly. The number of windows in a building may vary from one room to another and from one building to another, making it random but not evenly distributed. The fairness concern arises because the method relies on the number of windows in the room to select a volunteer, and not all houses or rooms are equally likely to have the same number of windows. For fairness, it's preferable to use a selection method where each participant has an equal chance of being chosen, regardless of external factors like the number of windows.
(1 vote)
• I don't understand Abby's chance in the two-dice problem in the excercise. Why is it P? We only care about the total number of the two dices. The order should be irrelevant. It should be C, right?
(1 vote)
• Since the magician is trying to get each child to have an equal chance of being chosen, doesn't the fact that he starts from the birthday boy influence the entire process?
(1 vote)
• The fact that the magician starts from the birthday boy could potentially influence the selection process if the starting point is not chosen randomly. If the starting point is predetermined or biased, it may affect the fairness of the selection method by giving some participants a higher chance of being chosen than others. Therefore, it's essential to consider whether the starting point is random when evaluating the fairness of the method.
(1 vote)
• How to calculate a probability of choose 3 off-suited and off-ranked cards out of 4 given cards from a standard 52-cards deck.

E.g. you're dealt 3 cards at a time.

P.S. By simulating the situation on a computer (1mln tryies) the answer must me like 54.5%)

P.P.S. The same question but to get 2 cards (off-suited and off-ranked)
P.P.S. The same question byt 1 card (off-suited and off-ranked) or what is the same 3 cards either same suit or same rank
(1 vote)
• I am quite confused as to what you are actually asking here. You say you want 3 off-suit, off-rank cards out of 4 but then say you are dealt 3 cards at a time. Can you give an example of what would be a "success"?
(1 vote)
• Regarding "Using probability to make fair decisions" exercise 1: Peter, Austin, Jason, and Matt each want a different type of pizza

The question does not specifiy whether cards are chosen without replacement or not. It should explain that first in the question.
(1 vote)
• In the exercise "Using probability to make fair decisions," the clarification about whether the cards are chosen with or without replacement would indeed be helpful in determining the fairness of the selection process. With replacement means that after each selection, the card is returned to the deck, while without replacement means that the selected card is not returned. The fairness of the selection process may vary depending on whether cards are chosen with or without replacement, as it affects the probabilities of subsequent selections. Therefore, specifying this detail would provide clarity in evaluating the fairness of the decision-making process.
(1 vote)