A thief has stolen Rogers automatic teller card. The card has a four digit perso

Question

A thief has stolen Rogers automatic teller card. The card has a four digit personal identification number (PIN). The thief knows that the first two digits are 3 and 5, but he does not know the last two digits. Thus, the PIN could be any number from 3500 to 3599. To protect the customer, the ATM machine will not allow more than three unsuccessful attempts to enter the PIN. After the third wrong PIN, the machine keeps the card and allows no further attempts.

1.) What is the probability that the thief will find the correct PIN within the the tries? ( Assume that the thief will not try the same wrong PIN twice.)

2.) If the thief knew that the first two digits were 3 and 5 and that the third digit was either a 1 or 7, what is the probability of guessing the correct PIN in 3 attempts?

Explanation / Answer

1) as for last 2 digits we have 100 choices and been given 3 attempts

probability that the thief will find the correct PIN within the the tries =3/100=0.03

2)as last 2 digits are costricted to 20 probable values if third digit is 1 or 7

hence probability =3/20=0.15

please revert

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