Question 468417: I cannot for the life of me figure this one out, I have tried several time and still come up with the wrong answer. The questions is:
The access code for a garage door consists of three digits. Each digit can be 2 through 7 and each digit can be repeated.
a)Find the number of possible access codes
b)What is the probability of randomly selecting the correct access code?
c)What is the probability of not selecting the correct access code?
Thank you
Found 2 solutions by Alan3354, Theo:
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! The access code for a garage door consists of three digits. Each digit can be 2 through 7 and each digit can be repeated.
a)Find the number of possible access codes
2 thru 7 = 6 numbers
6^3 = 216 codes
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b)What is the probability of randomly selecting the correct access code?
1/216
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c)What is the probability of not selecting the correct access code?
215/216
Answer by Theo(13342)  (Show Source):
You can put this solution on YOUR website! there are 6 digits from 2 through 7.
they are: {2,3,4,5,6,7}
The number of possible access codes are 6^3 = 216
The probability of randomly selecting the correct access code is (1/6)^3 = 1/216.
The probability of not selecting the correct code is 1 - 1/216 = 215/216.
I can't show you all the codes because there are too many.
I can, however, show you a much simpler situation.
suppose the possible digits are 3 and 4.
That's 2 possible selections per digit.
With repetition of digits, the number of possible combinations are 2^3 = 8
Those possible combinations are:
111
112
121
122
211
212
221
222
The probability of randomly selecting the correct code is (1/2)^2 which becomes 1/8.
Assume the code is 211.
You can see that there is only 1 code out of the 8 possible codes that contains 211.
The probability of selecting 211 randomly is therefore 1 out of 8.
The probability of NOT selecting the correct code is 1 - 1/8 = 7/8.
You can see that there are 7 out of 8 codes that do not contain 211.
With 6 possible numbers per digit, the number of possibilities is much greater and the probability of guessing the correct code is also much smaller.
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