Statistics and Probability pls help : (

Question

An inventor created a machine where you can input a string of 4 letters and expect an output from it. If you input any of the letters S, C, or D, the probability that the output of the letter inputted is x=0.46, and the probability that it is one of the two letters is (1-x)/2. The machine allows you to input one of the three-letter strings SSSS, CCCC, and DDDD, with probability 0.25, 0.44, and 0.31 respectively, but there is a possibility that the output could be any possible 4 letter combinations of S, C, and D. Each input is independent.

One person dared you to guess the original string of letters inputted from the output of SDCS. If you manage to guess it correctly, you will be promoted to become her right-hand man. You, a very competitive mathematician, will try to answer this strategically. Create the probability distribution of possible letter string inputs that will yield SDCS and determine the most probable letter string input that will yield an output of SDC.

Answer 1

Hi Rei A., Sorry, your input has resulted in a zero probability of anyone figuring out what you mean, hence a zero probability of correct output. 1) "the probability that the output of the letter inputted is" phrase lacks a verb, at the very least, or perhaps an object, 2) "that it is one of the two letters" -- why two, and which two? 3) "the machine allows you to input" -- how does the machine control your input probability?? 4) "Each input is independent" -- do you mean, you may mix the input letters as you like? 5) "there is the possibility that the output could be" -- do you mean that the output is limited to only the letters S,C, or D? 6) "will yield an output of SDC" does not match earlier text "SDCD"? 7) additionally, it is not clear if the 3 quoted probabilities are for results of S, C, and D respectively or for 4-letter phrases of SSSS, CCCC, and DDDD respectively.

Please rework the entire question to make it unambiguous!

-- Cheers, --Mr. d.