Question

Outside a​ home, there is aa 44​-key keypad numbered 11 through 44. The correct sevenseven​-digit code will open the garage door. The numbers can be repeated in the code. ​(a) How many codes are​ possible? ​(b) What is the probability of entering the correct code on the first​ try, assuming that the owner​ doesn't remember the​ code? ​(a) The number of possible codes is nothing. ​(Type an integer or fraction. Simplify your​ answer.)

Answer 1

Answer:

a) The number of possible codes is 16384

b) The probability of entering the code on the firs ttry is 1/16384

Step-by-step explanation:

a) For each of the four digits we have 7 possibilities and the number of one digit doesnt make restrictions on the others, thus, we have to power 4 a total of 7 times. The number of codes available is 4⁷ = 16384

b) There is only 1 code favourable over a total of 16384, as a consequence, the probability of enter the code correctly is 1/16384