A transaction ID generator generates random, 27 character strings from the set of lower case and upper case letters and single digits (a-z, A-Z, 0-9). A software bug causes the software to error out if the transaction ID contains the particular substring 'ABC' anywhere within the transaction ID. What proportion of transaction ID's generated will cause the bug?
Without any character repeating
okay we have [ABC] and 59 other characters to choose from to make a string of 27 (24+3)
(25*59P24) / 62P27
25*nPr(59,24)/nPr(62,27) = 0.0001101709853693
approx 1 in 10,000
I think that is correct.
and the 28 in my last answser that was wrong anyway shoud have be 25 - silly me.
Hello Alan: Can the font of your software package be made a little larger?
Even with eye glasses, my eyes have a rough time reading your answers! Thanks.
Hi Alan,
I am not saying your answer is wrong - I am just not necessarily convinced it is right.
Here is another possibility (probably wrong)
Say we stick an ABC together so that instead of choosing 27 characters we choose 24 plus our one lot of joined letters.
Then the answer could be
\(\frac{28*62^{24}}{62^{27}}=\frac{28}{62^{3}}=\frac{28}{238328}\)
28/238328 = 0.0001174851465208
So that is about 1 in 10,000
Much more often than what Alan got.
I do not think that this is correct because The ABC could occur in our not prejoined together sequences. So I tend to think it would happen more often than this - not less. :///
idk probability is so confusing LOL
Without any character repeating
okay we have [ABC] and 59 other characters to choose from to make a string of 27 (24+3)
(25*59P24) / 62P27
25*nPr(59,24)/nPr(62,27) = 0.0001101709853693
approx 1 in 10,000
I think that is correct.
and the 28 in my last answser that was wrong anyway shoud have be 25 - silly me.