The probability of getting both right the first time is easy: 0.25*0.25 = 0.625 or 6.25%
The probability of getting exactly one right is: either you get the 1st one right and miss the second, or vice versa. Thats 0.250.75 + 0.750.25 = 0.50.75 = 0.375 or 37.5%, so the probability of getting at least 50% is 0.375 + 0.0625 = 0.4375 or 43.75%, even without retries, so pretty good odds. The probability of missing both is 1 - 0.4375 = 0.5625 (or 0.750.75).
When you retry, there’s two possibilities:
You missed both: now your probability of getting at least one of them right is: (1/3)(1/3) + 2*(1/3)(2/3) =~ 55.55%
You got only one wrong: you just need to guess the other, so it’s 100% for you to get at least one, and 1/3 (33.33%) to get both
So, including a retry, you either:
Guess them both the first try: 0.0625 or 6.25%
Guess one of them, then guess both: 0.375*(1/3) = 0.125
Guess one of them, then still guess only one: 0.375*(2/3) = 0.25 or 25%
Guess none first, then guess one: 0.56252(1/3)(2/3) = 0.25 or 25%
Guess none first, then guess both: 0.5625*(1/3)*(1/3) = 0.0625 or 6.25%
Guess none, then still guess none: 0.5625*(2/3)*(2/3) = 0.25 or 25%
So, probability of a passing grade is 75%. Not a very good test if it’s so easy to pass by random guessing ;)
P(passing) = 1- P(failure)
P(failure) = P(failure first try)*P(failure second try)
P(failure first try)=(3/4)^2
P(failure second try)=(gonna post in reply)
P(failure second try)=(2/3)^2 since you can eliminate one choice but 2 others are still wrong.
To total:
P(failure)=(3/4)^2*(2/3)^2=1/4
1-1/4=0.75
So the probability of passing is 0.75
Edit:
Remark: this problem is elegant if you attempt to calculate the passing as the complement of failure rather than enumerate all successes. Shouldn't take more than 3 minutes with a clear head if you know the correct approach. If this was an college level intro probability exam question, it should be done the fast way since it's meant to eat up your time otherwise.
Not sure if it was a fever dream but probably more opiod medication related…
Its some combination of the following
some cartoon wedding segment
South Park?
there’s like a wedding song that gets cut off but it sort of sounds like this but its like an organ and I’m saying that because its possible I was playing that game a little while South Park was playing in background
its only like a 3-4 second motif and I feel like it plays a few times throughout
structurally its conjunct and it starts on the tonic,
Tool handles. If you apply a hard glossy coat they just become too damn slippery and if it’s summer it’ll often slip on your sweat and it feels all clammy.
Chopsticks for the same reason, I always find myself dropping my food like an idiot when they are glossy and laqcuered. Especially when I was at a restaurant and for whatever reason they had mirror finished steel chopsticks. What the fuck!
I often get subjected to some weird non-euclidean geometry that makes me dizzy. Of course I usually get dizzy from being sick, but my imagination makes my dreams really weird to explain why.
For lifestyle reasons, my sense of dreaming is very, very weak and can only remember one time I went to a school I didn’t go to as the most surreal. To be fair it looked like Hogwarts though.
During standardized testing, because I hated math, I always just bubbled in my answers at random on the Scantron and still got average marks for it like half the time.
Later in high school I also learned that in a multiple choice questionnaire, C is the most commonly correct answer so if you just answer C on everything your odds of getting a passing grade are pretty high. Legit were told to just answer C when we didn’t know in a class preparing us for an academic decathlon.
I’m not one of those ‘I hate children’ child free people, but I really love not having any kids of my own. There’s plenty of kids out there that need parental figures who’s need I can meet. My partner’s daughter is one of them, and I love the hell out of that kid.
But at the end of the day, I’ve still done better for the world by not bringing one of my own into it, for a multitude of reasons including climate change.
asklemmy
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