A thief steals an ATM card and must randomly guess the correct four-digit pin code from a 4-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 (Type an integer or fraction. Simplify your answer.)

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
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Chapter1: Starting With Matlab
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I need help solving this statistics problem.
**Problem:**

A thief steals an ATM card and must randomly guess the correct four-digit pin code from a 4-key keypad. Repetition of digits is allowed. What is the probability of a correct guess on the first try?

**Question:**

The number of possible codes is ____  
(Type an integer or fraction. Simplify your answer.)

---

In this problem, you are given a scenario involving a keypad with only four keys, and digits can be repeated. To determine the number of possible 4-digit codes, you need to consider the number of choices for each digit. 

Since each digit has 4 possible outcomes (due to the 4-key keypad), and there are 4 digits in the pin, the total number of possible combinations is calculated by multiplying the number of choices for each digit:

\[ 4 \times 4 \times 4 \times 4 = 4^4 = 256 \]

Therefore, there are 256 possible pin codes.

The probability of guessing the correct code on the first try is:

\[ \frac{1}{256} \]

This probability is calculated by considering that only one of the 256 possible combinations is correct, hence the chance or likelihood of randomly selecting that exact one is 1 out of 256.
Transcribed Image Text:**Problem:** A thief steals an ATM card and must randomly guess the correct four-digit pin code from a 4-key keypad. Repetition of digits is allowed. What is the probability of a correct guess on the first try? **Question:** The number of possible codes is ____ (Type an integer or fraction. Simplify your answer.) --- In this problem, you are given a scenario involving a keypad with only four keys, and digits can be repeated. To determine the number of possible 4-digit codes, you need to consider the number of choices for each digit. Since each digit has 4 possible outcomes (due to the 4-key keypad), and there are 4 digits in the pin, the total number of possible combinations is calculated by multiplying the number of choices for each digit: \[ 4 \times 4 \times 4 \times 4 = 4^4 = 256 \] Therefore, there are 256 possible pin codes. The probability of guessing the correct code on the first try is: \[ \frac{1}{256} \] This probability is calculated by considering that only one of the 256 possible combinations is correct, hence the chance or likelihood of randomly selecting that exact one is 1 out of 256.
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