Let's say I have a code for numbers made from a 4 x 4 matrix such that two letters match a number e.g.
I create a string of numbers using the code and hide them in the letters.
AA DD AD AA AD AB AA AC BA BB AB AC BC
The problem is, the code has become corrupted and now reads:
AA DD CD AA AD AD CA AC BA BB DB DC BC
A friend knows that the code has been corrupted, but makes some very good guesses at what might have been the 13 position number with seven number positions identified.
1.#14##356##7
What is the probability that my friend correctly guessed the 7 numbers and decimal? Secondly, given my friends result, what's the probability that the original number encoded was the square route of 2 (1.41421356237)?
It's unusual that one would be attempting to compare a number fragment to a larger reference number. Can you still multiply the probabilities of individual positions? In this case it would appear to be 1/4 chance of getting a letter correct, but 1/16 probability of correctly getting any one number.
Am I correct to assume that the probability of matching the 7 numbers and decimal is 1/16^8? Is there a general formula for working out such problems?
| A | B | C | D | |
| A | 1 | 2 | 3 | 4 |
| B | 5 | 6 | 7 | 8 |
| C | 9 | 0 | + | - |
| D | X | / | = | . |
I create a string of numbers using the code and hide them in the letters.
AA DD AD AA AD AB AA AC BA BB AB AC BC
The problem is, the code has become corrupted and now reads:
AA DD CD AA AD AD CA AC BA BB DB DC BC
A friend knows that the code has been corrupted, but makes some very good guesses at what might have been the 13 position number with seven number positions identified.
1.#14##356##7
What is the probability that my friend correctly guessed the 7 numbers and decimal? Secondly, given my friends result, what's the probability that the original number encoded was the square route of 2 (1.41421356237)?
It's unusual that one would be attempting to compare a number fragment to a larger reference number. Can you still multiply the probabilities of individual positions? In this case it would appear to be 1/4 chance of getting a letter correct, but 1/16 probability of correctly getting any one number.
Am I correct to assume that the probability of matching the 7 numbers and decimal is 1/16^8? Is there a general formula for working out such problems?
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