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:
[tex][\frac{1}{128}]^{150}[/tex]
Hence, the probability that all the codes are not unique is:
[tex]1-[\frac{1}{128}]^{150} \approx 1[/tex]
Because the value of [tex][\frac{1}{128}]^{150}[/tex] 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%.
