Question

3 residents enter an elevator in an apartment complex at the ground floor. They each press a button 1-10 (each resident presses the button that corresponds to his or her floor. The same button may be pressed several times). If each button is equally likely to be pressed, what is the probability that 3 consecutive buttons are pressed?

Answer 1

Answer:

The answer is %2,4

Step-by-step explanation:

Residents can press on 10 different button choice when they enters the elevator. Number of components for the sample space for the event is

$10*10*10=1000$

There are 8 different possibilities that 3 consecutive buttons are pressed those are:

-1,2,3

-2,3,4

-3,4,5

-4,5,6

-5,6,7

-6,7,8

-7,8,9

-8,9,10

When the pressing order doesn't matter, those buttons can be pressed 3 different ways for each possibility.

$8*3=24$

The probability is:

$24/1000=0.024$