Combination Lock A safe containing is locked with a combination lock. You pay for one guess at the six-digit combination. If you open the lock, you get to keep the million dollars. What is your expectation?
The expected value for the combination lock.
The compliment of the probability is given as,
Here, is the compliment of the probability and is the probability.
The expected value is given as,
Here, is the amount of payout and is the probability of payout.
A safe containing and for one guess at the six-digit combination you pay .
Since there is six digit combination in the lock, then the total possibilities are .
The probability of the safe will open is,
The probability of the safe will not open is,
Calculate the expected value of the game
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