Interesting question, what could be the solution the problem below?

Question

An ATM machine requires that a customer enter a four-digit personal indentification number (PIN) when using their ATM card. If a thief steals a customer card and tries to guess the PIN, what is the probability that the thief will succeed at the first attempt?

possible solutions...

1/ 990080

1 / 404600

1/ 109902204

1 / 10000

or is it none of the above ?

Answer 1

9x8x7x6x5x4x3x2x1 x1x2x3x4

Answer 2

There are 10 possibilities for each of four digits, so the probability of getting them all correct is 1 / 10^4 = 1 / 10000.

Actually, though, people tend not to pick very random numbers, so a smart thief could probably raise this somewhat.

Answer 3

Well if you take 4 being the amount of digits in the code, and take it to the power of 10, the amount of 1 digit numbers (0-9), you get 1048576. So their are 1,048,576 possible combinations. The odds of getting it on the 1st try would be 1/1,408,576.