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Question

A thief steals an ATM card and must randomly guess the correct four​-digit pin code from a 8-key keypad, repetition of digits is allowed. What is the probability of a correct guess on the first​ try?


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Solution

Step 1: Find the probability of guessing each digit correct.

The total number of keys on the keypad is 8.

The pin is of 4 digits.

We know that, the probability of an event is PE=PossibleoutcomesTotaloutcomes

The probability of guessing the first digit right is 18,

The probability of guessing the second digit right is 18,

The probability of guessing the third digit right is 18,

The probability of guessing the fourth digit right is 18,

Step 2: Find the probability of a correct guess of the pin.

To obtain the probability of a correct guess on the first​ try P(E), using the multiplication rule of probability.

PE=18×18×18×18PE=184PE=14096PE=0.00024

Hence, the probability of a correct guess on the first​ try is 0.00024.


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