3 ms·
Actually, it's not even close. 10,000 attempts to guess a 4-digit number are certain to succeed. 100 attempts to guess 100 4-digit numbers have a good chance of
by StephanTLavavej 10y ago
Actually, it's not even close. 10,000 attempts to guess a 4-digit number are certain to succeed. 100 attempts to guess 100 4-digit numbers have a good chance of resulting in no hits. For each 4-digit number, you produce 100 different guesses (with no repeated guesses for that number, because that would be silly). There's a 100/10,000 chance of a hit, and 9,900/10,000 chance of a miss. The chance of missing on all 100 4-digit numbers is (9,900/10,000)^100 = 0.366 = 36.6%. That's substantial!
Guessing 100 numbers, there's a chance to produce 2 or more hits, of course.
- caf 10y agoGuessing 100 numbers, there's a chance to produce 2 or more hits, of course. ..to the point that the expected value should converge to the same amount, right?
- kctess5 10y agoThe expected value of both strategies is to have 1 success, but they have different variance. The first strategy has variance of 0.99, and the second strategy has variance 0. The chance of n out of 100 hits with the first strategy is: binomial(100,n) x 0.01^n x 0.99^(100-n) edit: asterisks as multiplication signs => italics
- erikpukinskis 10y agoRight, but variance doesn't matter if you just repeat the scam tomorrow.