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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.

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 accou class=
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 accou class=

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musiclover10045

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

JeanaShupp

Answer:

  • If repetition is allowed then the number of ways of making a pass code =[tex]2600[/tex]

  • The probability of choosing the first digit correctly = [tex]\dfrac{1}{10}[/tex]
  • The probability of choosing the second digit correctly = [tex]\dfrac{1}{10}[/tex]
  • The probability of guessing letter correctly = [tex]\dfrac{1}{26}[/tex]

  • The probability that you would guess Hector's passcode correctly on the first try =[tex]\dfrac{1}{2600}[/tex]

Step-by-step 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 :-

[tex]10\times10\times26=2600[/tex]

The probability of choosing the first digit correctly = [tex]\dfrac{1}{10}[/tex]

Similarly , the probability of choosing the second digit correctly = [tex]\dfrac{1}{10}[/tex]

The probability of guessing letter correctly = [tex]\dfrac{1}{26}[/tex]

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 ;-

[tex]\dfrac{1}{10}\times\dfrac{1}{10}\times\dfrac{1}{26}=\dfrac{1}{2600}[/tex]

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