the game of mastermind starts in the following way: one player selects four pegs, each having six possible colors, places them in a line. the second player then tries to guess the sequence of colors. what is the probability of guessing correctly?
Am i missing something, but i woukd go about this by obtaining the sample space: $6^4$ but i feel there has to be more with regards to guessing correctly. I mean i suppose there is only 1 way of getting the right answer that is guessing the sequence. So probabikity would be $\frac {1}{6^4} $ I for some reason feel there may be more ways.
Best Answer
If you are guessing randomly, then yes, the probability of getting the sequence correct is just $6^{-4}$. You can think of guessing each peg one at a time. The probability of getting any peg correct is $6^{-1}$, and as an individual peg does not give you information on any other peg, the probability of getting all $4$ correct is just $6^{-1}\times 6^{-1}\times 6^{-1}\times 6^{-1}$.