Question

A keypad at the entrance of a building has 10 buttons labeled 0 through 9. What is the probability of a person correctly guessing a 9​-digit e

Answer 1

A keypad at the entrance of a building has 10 buttons labeled 0 through 9. What is the probability of a person correctly guessing a 9​-digit entry code if they know that no digits repeat?

Answer:

the probability of a person correctly guessing a 9​-digit entry code if they know that no digits repeat is 0.1

Step-by-step explanation:

We know that probability= number of required outcomes /number of all possible outcome.

From the given information;

the number of required outcome is guessing a 9-digit = 1  outcome

the number of all possible outcome = ¹⁰C₉ since there are 10 numbers and 9 number are to be selected.

Since there are only 9-digit that opens the lock;

the probability of a person correctly guessing a 9​-digit entry code is

$P =\dfrac{1}{^{10}C_9}$

$P =\dfrac{1}{\dfrac{10!}{9!1!}}$

$P =\dfrac{1}{10}$

P = 0.1