Aplanned community has 150 homes, each with an automatic garage door opener. the door opener has seven switches that a homeowner can set to 0 or 1. for example, a door opener code might be 1001100. assuming all the homes in the community are sold, what is the probability that at least two homeowners will set their switches to the same code, and will therefore be able to open each other's garage doors?

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%.

10000000000000000000000000000000

-3

step-by-step explanation:

a drawing really does here:

so i draw the horizontal line y=2 and the vertical line x=-2 at this intersection i put b (this is where my right angle is going to be).   so point b is at (-2,2).   point a is 5 units long and is also on y=2 so this point has to be (3,2) or (-7,2) -doesn't matter i will go with (3,2).

now we know c is at (-2,y) we don't know the y yet bet we know that c is on x=-2.

we have the area of the triangle is .5bh=12.5

we know the base length is 5 (ab)

we have the height is (2-y) if you look at your

plug in

.5(5)(2-y)=12.5

solve for y to get the y-coordinate for c

2.5(2-y)=12.5

divide both sides by 2.5 giving:

2-y=5

now subtract 2 on both sides

-y=3

y=-3