QQuestionAnatomy and Physiology
QuestionAnatomy and Physiology
A thief steals an ATM card and must randomly guess the correct five-digit pin code from a 10 -key keypad. Repetition of digits is allowed. What is the probability of a correct guess on the first try?
The number of possible codes is $\square$.
(Type an integer or fraction. Simplify your answer.)
The probability that the correct code is given on the first try is $\square$.
(Type an integer or fraction. Simplify your answer.)
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Answer
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Step 1
Number\,of\,possible\,codes = 10 \times 10 \times 10 \times 10 \times 10 = 10^5
To find the total number of possible five-digit pin codes, we need to determine the number of choices for each digit. Since the thief is guessing randomly, any digit from 0 to 9 can be used for each position. This results in 10 choices for each of the five positions.
Step 2
Probability = \frac{Number\,of\,successful\,outcomes}{Total\,number\,of\,possible\,outcomes} = \frac{1}{10^5}
Now, to calculate the probability of a correct guess on the first try, we divide the number of successful outcomes (guessing the correct code) by the total number of possible outcomes (all five-digit codes).
Final Answer
The probability that the correct code is given on the first try is $\frac{1}{10^5}$.
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