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Answer:
The probability that at least two homeowners will set their switches to the same code is 100%.
Step-by-step explanation:
Consider the provided information.
The total number of code can be set with 0 or 1 is:
2×2×2×2×2×2×2=128
There are 128 different codes.
The probability that code is unique is 1/128
Now, the probability that all codes are unique is:
Hence, the probability that all the codes are not unique is:
Because the value of is very small
As they can set 128 different codes and there are 150 homes. So, at least two homeowners will set their switches to the same code is 100%.
Hence, the probability that at least two homeowners will set their switches to the same code is 100%.