A bank lobby has four video cameras positioned to view the entire lobby. any one of the four is sufficient to monitor the lobby. each camera functions independently and has a reability of 0.90, that is, the probability of functioning is 0.90. a bank robbery takes place. let a success (x) be defined as a camera functioning. find the probability that the robbery was filmed at least by one acamera.

To find the probability that the robbery was filmed by at least one camera, we need to calculate the probability that none of the cameras functioned and subtract it from 1.

Let's break down the problem step by step:

Step 1: Find the probability that a single camera did not function.
The probability that a single camera does not function is 1 - 0.90 = 0.10.

Step 2: Find the probability that all four cameras did not function.
Since the cameras function independently, the probability that all four cameras did not function is (0.10)^4 = 0.0001.

Step 3: Find the probability that at least one camera functioned.
The probability that at least one camera functioned is 1 - probability that all four cameras did not function.
So, the probability that at least one camera functioned is 1 - 0.0001 = 0.9999.

Therefore, the probability that the robbery was filmed by at least one camera is 0.9999 or 99.99%.

To summarize the steps:
1. Find the probability that a single camera did not function: 0.10
2. Find the probability that all four cameras did not function: (0.10)^4 = 0.0001
3. Find the probability that at least one camera functioned: 1 - 0.0001 = 0.9999 or 99.99%