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Alex_Xolod [135]
3 years ago
7

Outside a​ home, there is aa 44​-key keypad numbered 11 through 44. The correct sixsix​-digit code will open the garage door. Th

e 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?
Mathematics
1 answer:
olya-2409 [2.1K]3 years ago
5 0

Answer:

a) 4,096

b) 0.000244

Step-by-step explanation:

a)  

By the Fundamental rule of counting, there are

4*4*4*4*4*4 = 4,096  

ways of forming six-digit arrangements where each position has 4 possibilities (1 to 4)

b)

The probability of entering the correct code on the first try, assuming that the owner does not remember the code is  

1/4096 = 0.000244

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