Is the psa slab authentic , the spacing between the first 4 number is closer but 1 7 1 3 seems further apart?
How to tell for sure a slab is authentic?
How to tell the different generation of slab? They said to look like first 2 cert number?
(Censor price as not to cause unnecessary problem to seller)
How to be smarter? (Not in a IQ manner, but how to be better in these kind of things?)
Genuine post, please advice
Encountered a very common Qn:
A fair coin is flipped repeatedly. What is the expected number of flips required to get 3 heads in a row (HHH)?
I answered 8. (Wrong)
I read an answer:
“
How I'd do it is to think in terms of attempts. Every attempt to flip three heads in a row ends as soon as you flip a tails and you must then start the next attempt.
Each attempt is then one of the following:
T - 1/2
HT - 1/4
HHT - 1/8
HHH - 1/8
The expected number of flips per attempt is then
(1 * 1/2) + (2 * 1/4) + (3 * 1/8) + (3 * 1/8) = 14/8
The expected number of attempts to achieve something with a probability of x is 1/x. It takes an average of two flips to get a (single) heads; it takes an average of six rolls of a die to get a 6, etc.
So you have 1/(1/8) * 14/8 = 8 * 14/8 = 14
“
But still took me 1+ Hour to fully understand.
How I understood is:
Why 8 is wrong answer? Probability is 1/8 -> expected is 8. But this is wrong because "each trial" is not independent. "THHTHHH" is a valid case. The answer can be within a “sliding window”.
The trick is like what the answer said, group it into an attempt. This makes "each attempt trial" independent.
So the probability to get a successful attempt is 1/8 -> 8 attempt needed.
But the average number of flip per attempt is 14/8 -> so average number of flip is 14/8 * 8 = 14
(But even saying that I "understand", I am not confident that if someone tweaks the question, I'll 100% be able to answer)
So here's a question to the geniuses here:
How do you be smarter?
How do you read the solution once and fully understand it?
how to fully understand the concept such that even if there is a twist/variation you will still 100% know the answer?
(Context: am a young 20s SWE , grad from T10)