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Homework answers / question archive / A typical "combination" lock is opened with the correct sequence of three numbers between 0 and 49 inclusive
A typical "combination" lock is opened with the correct sequence of three numbers between 0 and 49 inclusive. (A number can be used more than once.) What is the probability of guessing those three numbers and opening the lock with the first try?
The chances of guessing the first number is one out of 50 (0 to 49- so you have 50 possible numbers), or 1/50
Since we can repeat the same number in the combination, the chances of selecting the correct second number is also 1/50
and obviously this is also the probability of selecting the third number correctly.
Since we need all three guess to be correct - this is an "AND" system, which means that the first guess AND the second guess AND the third guess must be correct in order to open the lock.
Therefore the overall probability is the product of the probabilities to guess each number separately:
P = 1/50 * 1/50 * 1/50 = 8E-6 = 8 * 10 ^(-6)
