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
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.
