Question 1076837: A thief steals an ATM card and must randomly guess the correct five
-digit
pin code from a 9
-key
keypad. Repetition of digits is allowed. What is the probability of a correct guess on the first try? And number of possible codes?
Found 3 solutions by Boreal, jim_thompson5910, stanbon:
Answer by Boreal(15235)   (Show Source):
Answer by jim_thompson5910(35256)  (Show Source):
You can put this solution on YOUR website! I'm going to work in reverse. To find the probability, we first need to know how many possible combinations there are. Once we know that, we can find the probability of guessing the right code on the first try.
We have 5 slots and 9 choices per slot. Because repetition is allowed, we multiply out the number of choices per slot
The longhand form would be 9*9*9*9*9 basically five copies of "9" multiplied together. This is a bit tedious so it's better to write it in exponential form 9^5 which is the same thing, just much more compact. In any event, use a calculator to find that
9^5 = 9*9*9*9*9 = 59,049
So there are 59,049 different combinations. Only one combination is the proper code, so the probability of getting the right code is 1/59049 in fraction form (1/59049 = 0.0000169350878 in decimal form)
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To recap,
Question: What is the probability of a correct guess on the first try?
Answer: 1/59049 in fraction form, which is equivalent to 0.0000169350878 in decimal form
Question: Number of possible codes?
Answer: 59,049
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website! A thief steals an ATM card and must randomly guess the correct five
-digit
pin code from a 9
-key
keypad. Repetition of digits is allowed. What is the probability of a correct guess on the first try? And number of possible codes?
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Assuming 9-key mean zero up to 9,
# of possible codes = 10^5 = 100000
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Probability of first try correct = 1/10^5
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Cheers,
Stan H.
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