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?

Answer 1

The probability is 1/4096.

Since repetition is allowed, each digit could be any of the 8 on the keypad; this makes the number of choices 8*8*8*8 = 4096.  Only one of those is correct, so the probability is 1/4096.

Answer 2

The probability of a correct guess on the first try is 0.024%.

Since a thief steals an atm card and must randomly guess the correct four -digit pin code from a 8 -key keypad, and repetition of digits is allowed, to determine what is the probability of a correct guess on the first try the following calculation must be performed:

• 8 x 8 x 8 x 8 = X
• 8 ^ 4 = X
• 4096 = X
• 1/4096 = X
• 0.000244140625 = X
• 0.000244140625 x 100 = 0.024%

Therefore, the probability of a correct guess on the first try is 0.024%.

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