With one scan cycle of a radar tracking a space object, the object is detected with a probability of 0.75.

With one scan cycle of a radar tracking a space object, the object is detected with a probability of 0.75. The detection of an object in each cycle occurs independently of the others. Find the probability that after 3 cycles the object will be detected.

The probability of detecting an object in one cycle is p = 0.75.
The probability that the object will not be detected: q = 1 – p = 1 – 0.75 = 0.25.
The probability that for all three cycles the object will not be detected:
P (0) = q ^ 3 = 0.25 ^ 3 = 0.0156.
The probability of an opposite event such that the object will be detected at least once:
P` (0) = 1 – P (0) = 1 – 0.0156 = 0.9844.
Answer: The probability that the object will be detected is 0.9844.