So it would be the 22nd number. Or -21. (n-21). 157 - 21 = 136
hmm isn’t that (n - 22 + 1) = n - 21?
Yup. How did you figure that out? What is it in terms of k?
Its (n-k+1). How’d I figure it out? Hmm. Well I kinda noticed that before:
I ended up thinking it may have to do with nature of factorials:
But idk.
Also I noticed that thinking of it in terms k + 1 still kinda confuses me, but thinking of it in terms -k + 1 I think makes more sense.
How did you figure out the 136 or -21? I’m guessing you didn’t get them from the n-k+1 formula.
Hmm your right. My original answer than was not based on finding it from n-k+1 formula.
mmmmm. oh yea:
My thought process was I noticed it subtracting. We would multiply 22 terms here. So the last term would be n - (22 - 1) . hmm i guess that could be shown as n - (k-1). ;o is that where the k+1 comes from. n - (k-1)= n- k +1.
Yeah. Why did you put a - 1 in
n - (22 - 1)
You asked how I get -21/136. It was using that formula(?). I didn’t use n-k+1. I did use, due to noticing it, that the last term would be k - 1 or n - (k - 1) . I did n- (22-1) to get the -21. Though I guess this is more explicit(?) then what was going through my head. I noticed thats what I did after the fact, when you asked me.
Hmm. Guess that didn’t directly answer it, Why?:
I noticed the last term, in that case 22, was subtracted by 1 before subtracting it from n.
You’re trying to multiply k things. Why is there an adjustment of 1 instead of just using k? How would you explain it to someone?
Hmm.
You do end up multiplying k things. The last value gets subtracted by k - 1 because we start from just the first value(?) and end up subtracting -1 starting from the second value. Or:
A permutation of just k = 1 is just the objects. So if you had P(157,1), it would equal just 157. You have 157 different permutations. If you had P(157, 2) you have 157 x 156. You subtract to get the second term value.
Hmm. I’m having trouble explaining this better. Idk if this is fine. Oh yeah I guess it would work for the first time too since n - 1 + 1 = n.
If you count from X to Y, inclusive, how many numbers did you count? Figure out a formula.
1, 2, 3, 4, 5. Counted five numbers from one to five. Ok.
Well 5 - 1 is 4. if you add 1 you get 5.
3 4 5 6 7 8 9. Counted seven numbers from three to nine.
9 - 3 = 6. Add 1 you get 7.
I think from x to y, if you do:
y - x + 1 you will get the number of terms counted.
Can you explain why there’s a +1 in there?
Can you connect this answer with the issue about permutations we’ve been discussing?
From 12.5 Conditional Probability and the Hypergeometric Probability Distribution Model:
Ok. Why did we reduce the sample space? There’s no TT anymore. Oh because the original sample space includes TT, but the two probabilities/events we’re looking out just deal with heads in some manner. Either two heads (event E) or at least one head (event F) so they’re just reducing the sample space to what we’re actually dealing with.
Yes. Intersection seems to be like “and”. When does E and F happen.
Heh. Why are we dividing by n(F)? Hmm. Probability is an event divided by the sample space. So we have the event (both E and F occurring) divided by the sample space that we defined earlier as n(F). Or I guess we didn’t define it. We would just consider the “reduced” sample space represented by F.
Conditional? What we got here is E and F happening at the same time, and F happening. Hmm.
So its conditional probability of E (or whatever the first event in the notation is) given the probability of F. So is it the probability of E in the second event/sample space of the other event?
(they had a thing listing out the dice rolls)
a.) probability of E is 11/36, probability of F is 3/36
Ok so we’re finding the probability of F given E. The probability of two dice adding to 4 given the sample space of events that the at least 1 die shows a 1.
so e and f happen twice, n(e) is 11. so 2/11
b) again e and f is two. n(f) = 3 so 2/3
hmm. so long as theres an intersection of probabilities. wouldn’t there always be some conditional probability?
Kinda?
In my head its something like this:
You have two numbers y and x. When you subtract y and x, the difference you get tells you how many numbers are between x and y. You need a +1 to make it inclusive. I’m having trouble explaining it better than that.
they look similar first of all. n - k + 1, and y - x + 1
mmm. im a bit tired so im having trouble coming up with some of way to explain the connection. ill try tomorrow morning.
What is subtraction? How does it work? When you subtract A-B=C, what do A, B and C represent or mean in words? Give all the answers you know.
Hmm.
First answer: subtraction is removing a quantity from another quantity. In A-B=C, A represents an initial quantity B represents an amount to be removed from that initial quantity and C represents the remaining value after removing that quantity.
I guess as a second answer (or maybe they’re the same) I’ve heard stuff like subtraction understood as above is not a thing and what actually exists in just adding negative numbers. I don’t get this point of view but in A-B=C, A represents the initial quantity, B represents, or -B I guess, represents some negative quantity you’re adding to A. C is the final value after adding B to A.
The final answer I have: subtraction is going down a number line from a value? So in A-B = C. A is where you’re starting from on the number line. B/-B is how many units(?) lefts you’re going on the number line from the initial value. C is where you end up on the number line.
Have you heard of subtraction finding the difference between two numbers?
Mmm. I think so? I’ve heard the the resulting value from subtraction be called the difference, yes. The three examples I shared above are the only ways I’ve really thought about subtraction. I’ve never taught subtraction or talked about it that much but I think I would, out of habit(?), call the resulting value the difference without giving it that much thought.
Can you explain why it would be called the “difference”?
Hmm. So in 5-3=2, 2 is the difference between 5 and 3. Its the value difference(?) between 5 and 3. So instead of talking about quantities getting removed, we’re talking about the gap in value between two numbers.It takes 2 to get to 5. Thats the difference?
I’m kinda unsure on this.