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.

The ATM card contains four-digit pin code. There are 4-key keypad.

Answered: A thief steals an ATM card and must…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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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.)