We're playing a game. I flip a coin. If it lands on Tails, I flip it again. If it lands on Heads, the game ends.
You win if the game ends on an even turn, and lose otherwise.
Define the following events:
A: You win the game
B: The game goes on for at least 4 turns
C: The game goes on for at least 5 turns
What are P(A), P(B), and P(C)? Are A and B independent? How about A and C?
Date | Post |
---|---|
2024-05-07 | Find a+b |
2024-05-09 | What is the area of the shaded region? |
2024-05-15 | Solve for x |
2024-05-17 | Bounding a function |
2024-05-22 | Coin-flipping game |
The image is of a large unit square with five smaller disjoint shaded squares contained entirely within it. The five smaller squares are congruent. Four of them are at each corner of the large square. The fifth is in the center, rotated diagonally, so the center of each of its sides is touched by the vertex from one of the other four squares. You are given that the common length for the five smaller congruent squares is (a-sqrt(2)) / b, where a and b are positive integers. What is the value of a + b?
I read this article and still walked away feeling like I didn't understand the situation that well.
Is it $56 billion that he's already been paid, and he needs to return it? $56 billion he's partially been paid, and he can keep what he has, but won't get the rest? Something more complicated?
Note that I'm using autohotkey v2, not v1.
I want to run two different autohotkey scripts. I want to trigger a hotstring in the first script, the output of which ends up being part of the hotstring trigger for the second script. Is this possible?
Here's a simplified version of my intended workflow.
Script 1:
#Hotstring EndChars \
#Hotstring o
#Hotstring ?
::iv::ǐ
::av::ǎ
Script 2:
#Hotstring EndChars \
#Hotstring o
#Hotstring ?
::nǐ::你
::hǎo::好
So the idea is that I can type niv\ and the first script will convert it to nǐ - then I can immediately type \ and the second script will convert it to 你. So I type niv\\ and my text goes from niv to nǐ to 你. I can then type hav\o\ and have my text go: h, ha, hav, hǎ, hǎo, 好. So I can do niv\ hav\o and get nǐ hǎo, or I can do niv\\ hav\o\ and get 你 好. Both writing systems in a reasonably simple format.
There are reasons I want to set it up like this. The first script has dozens of functions beyond writing in pinyin/chinese, and I share it with another person - so I don't want to add potentially hundreds of random Chinese hotstrings to it, just the special pinyin characters. That's why I'm using two scripts.
But I also realize I could just make "niv" and "havo" their own hotstrings which go directly to 你 and 好 without the intermediate nǐ and hǎo. I don't want to do this mostly because I think the system I have in mind is prettier - type it correctly in pinyin first, then have it correctly convert to Chinese.
All of that aside: I've gathered that this is probably possible using some combination of SendLevel and #InputLevel - but I've tried a bunch of different combinations and ideas with it, and haven't successfully had one script trigger another yet. Even in simplified toy scripts, which is a little discouraging. Ideally I'd be able to do this with as few changes to the main script I share with another person as possible - the script that handles the Chinese can be as complicated as it needs to be though. Anyone know how to make this work?
Imgur album: https://imgur.com/a/ikTA97e
Those photos were taken under extreme magnification and bright light - the actual size is about the size of an uncooked grain of rice. Maybe smaller. This one was killed by freezing to preserve its form.
In the last few days I've started to see a lot of these - I can find one crawling across my desk every 5 or 10 minutes if I remember to look (Though I can't find where they're coming from at all). They don't move all that fast - they're frankly pretty easy to capture or squash.
In person I don't think they look very much like ants but in the closeup I think they kind of do. Also hoping they aren't termites.
Thanks for any help.
Edit: Here's a video of one scurrying across my desk too: https://imgur.com/a/ZC15gNZ
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