A locker combination has three nonzero digits, and digits cannot be repeated. The first two digits are 9 and 8. What is the probability that the third digit is 7?
2 digits used, so 1/7 chance of any particular 3rd digit
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To find the probability that the third digit is 7, we need to consider the total number of possible combinations and the number of combinations that meet the given condition.
First, let's calculate the total number of possible combinations. Since the first two digits are fixed (9 and 8), we only need to consider the third digit. Since each digit can only be used once and we have 10 digits (0-9), the number of possible third digits is 10 (0, 1, 2, 3, 4, 5, 6, 7, 8, 9).
Next, we need to determine the number of combinations where the third digit is 7. Since the first two digits are fixed (9 and 8), and the third digit must be 7, there is only one possible combination that meets this condition, which is 987.
Therefore, the probability that the third digit is 7 is given by:
Probability = Number of combinations where the third digit is 7 / Total number of possible combinations
Probability = 1 / 10 = 1/10 = 0.1
So, the probability that the third digit is 7 is 0.1 or 10%.