Question

An extra security passcode for a certain account is made up of 2 digits followed by 1 letter. The digits may be the same. Hector chooses a passcode for this account. Enter values to answer the questions below.

Answer 1

• If repetition is allowed then the number of ways of making a pass code =
  `2600`

• The probability of choosing the first digit correctly =
  `(1)/(10)`

• The probability of choosing the second digit correctly =
  `(1)/(10)`

• The probability of guessing letter correctly =
  `(1)/(26)`

• The probability that you would guess Hector's passcode correctly on the first try =
  `(1)/(2600)`

Explanation:

Given: An extra security pass-code for a certain account is made up of 2 digits followed by 1 letter.

The number of choices for first and second place =10

The choices for the third place 26

If repetition is allowed then the number of ways of making a pass code is given by :-

`10*10*26=2600`

The probability of choosing the first digit correctly =
`(1)/(10)`

Similarly , the probability of choosing the second digit correctly =
`(1)/(10)`

The probability of guessing letter correctly =
`(1)/(26)`

If we choose the digits and letters randomly , then the probability that you would guess Hector's passcode correctly on the first tr4=y is given by ;-

`(1)/(10)*(1)/(10)*(1)/(26)=(1)/(2600)`

Answer 2

There is 10 digits to choose from and 26 letters.

Multiply the 3 choices together for total combinations: 10 x 10 x 26 = 2600.

The probability pf picking the first digit would be 1/10

The probability of picking the 2nd digit would also be 1/10

The probability of picking the letter would be 1/26