Y=the number of pins your opponent guess correct in the first round. Find P(Y=0) and P (Y=1).
In the game mastermind there are 8 different colours. 4 pins are used to make different codes. X is different colours that are used in a random code.
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Okay, for the opponent to guess everything wrong (Y=0), he first guesses the first pin wrong. There's a 7/8 chance of that happening. Same for the 2nd, 3rd, and 4th. So we have
I'll let you multiply that out!
For Y=1, think about the chance that the first pin was correct and the other three were wrong:
We would add this to the chance that the second pin is the only correct one:
And so on, four times, so we have
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