 # Week2: selecting 2 random people from 10 in video why probability

ways of selecting 2 random people from 10 should be 45 not 90 as we just use combinations not permutations. there is no fixed order of selecting each person as long as we are selecting any two people to be sample. please correct me if i am wrong. but 10k choose 100 was correctly given

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Correct reasoning. It should be 45 and not 90, because ordering would not matter in this case. I didn’t notice it yesterday when I asked a doubt related to this same video but I corrected it now. Thank you for pointing out.

I also got overflow error when calculating 10k choose 100 so i used wolframalpha

Same method I used then too

Have you seen bumrah’ bowling hypothesis???I have doubts regarding the way prof reasoned those statements. I should be rejecting hypothesis if there was 25% of getting samples which contradict my hypothesis or if only 75% chance of getting samples that are in favour. I would only accept my hypothesis if there is only 0-4% chance of getting samples that contradict(for now i don’t know true mean of total ball speeds. I only have some samples not total. I only looked at their means). The way they framed their reasoning opp to what we see. (infavour and not in favour). why would you reject something by giving a statement that is in favour of that.

I am not yet come across the Bumrah’s bowling hypothesis that you are talking about. Let see if someone else join this discussion to discuss about the same.

i think u should rewatch the lecture and pay attention to the plot representing mean for different samples. what prof said was " i reject the hypothesis bcoz there is a 25% chance that the sample he selects has a mean greater than 90 even though the true mean of the entire population is less than 90". if u look at the plot representing means, u ll see that the curve peaks in a region with less than 90. so the true mean must be less than 90. but the region for greater than 90 is not so small that we can neglect it. so there is a reasonable chance that the sample we select is from greater than 90 region. hence the hypothesis is refuted.

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Maybe u should read what i wrote because i know true mean will actually be less than 85. Based on plot shown i assumed occurrences of 85 to be 16 and occurrences of remaining means to be based on above assumption and approximating graph. I got more than 90 to be 17%. My problem is not about calculations.
The hypothesis is bumrah bowls with mean speed greater than 90. What i wanted to say is why would u reject a hypothesis by stating 25% that he bowls more than 90. U should be rejecting it by saying there is 75% chance that he bowls less than 90 not the other way.

From what i can make of, they should have hypothesis as bumrah bowls less than 90mph. and then rejected it by saying " I reject hypothesis because there is 25% chance of obtaining samples that are greater than 90mph even though true mean is less than 90mph.(What it says is i only got my samples in which 25% of getting a sample greater than 90mph. So cannot say this hypothesis works as u should be atleast 98% sure to be saying that. I don’t care what true mean is because i don’t know what its value is)
You can even see yield hypothesis and it also doesn’t make sense.

Hiee!!
I think the instructor wants to say that the percentage of getting a sample which is in favour of my hypothesis( i.e the mean of Bumrah’s bowling speed is more than 90 mph) while the true mean may be less is 25% . This 25% is very large for a hypothesis which is in contradiction to the true parameters of my population. Hence, I reject this hypothesis.

Hope that helps!!

I think, the video must be updated to avoid such confusions.

Thought of sharing my understanding of the topic which could help someone, or correct myself in case wrong.

Taking a non-sport example; like marks of students in a physics exam.
SomeOne wants to find the average marks scored by students of a particular class. Assume that the class strength is 100 and average is 75% but that SomeOne does not know this average.
Inorder to calculate the average instead of asking marks of all 100, SomeOne decides to ask just 10 students and calculate the average. Now he computes the average as 85%, [remember that he does not know the true average].
Now the average he computed is 85% which is his hypothesis, but can he trust this hypothesis? He decides to find if he could have gone wrong. (For simplicity lets assume this case), He asks the chemistry teacher how many students for the class are briliant. The chemistry teacher says that 30 students out of hundred are topper and scores 90% and above always. Now out of hundred 30 students are expected to get around 90%. which is 1/3 of the class. So there is high probability that the students to whom he asked marks toppers, which is 1/3 or 33.33% Which conveys each student he asked has a probability of 33.33% being brilliant. Now he thinks that this could have happened (remember he doesn’t know actual average). SomeOne rejects his hypothesis since he knows that there is large possibility that he could have gone wrong, since majority of 10 students he asked could easily be toppers. So he has to figure out some other way to arrive at more confident hypothesis

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