Answer to Question #124338 in Statistics and Probability for Yasini

Question

An automatic teller machine requires that each customer enter a four-digit personal identification number (PIN) when he/she insert a bank card. If person finds a bank card and guesses at a PIN to use the card fraudulently.
(I) what is the probability that a person will succeed in guessing in one attempt?
(II) if the person knows that PIN Will not have any repeated, what the probability that the person will succeed in guessing in one attempt?

Answer 1

(i) we have 10 numbers 0-9 and so each trial, the probabilty of picking the correct letter is 1/10 and there are four independent picks.

the probability of four correct picks = 1/10*1/10*1/10*1/10= 1/10000 = 0.0001

(ii) For a pick without repcament or without repeating the number picked 1/10*1/9*1/8*1/7 = 1/5040 = 0.0002