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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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Step 1

Number of possible codes=10×10×10×10×10=105Number\,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=Number of successful outcomesTotal number of possible outcomes=1105Probability = \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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