A signal is transmitted over a noisy channel. It is known that the signal will be correctly received with probability 0.797. If 3 copies of the signal are independently sent over this channel, what is the probability that at least one of them is received correctly?
My thought process is, if we are only looking at ONE signal being received correctly, the answer should be 0.797. However, I keep getting the answer wrong. Help!!
see earlier submission
To solve this problem, we need to find the probability that at least one of the three copies of the signal is received correctly. Let's break it down step by step:
1. Determine the probability that a single copy of the signal is not received correctly. Given that the probability of correct reception is 0.797, the probability of incorrect reception is 1 - 0.797 = 0.203.
2. Now we need to find the probability that all three copies of the signal are not received correctly. Since the copies are sent independently, we can multiply the probabilities. So, the probability of all three copies not being received correctly is 0.203 * 0.203 * 0.203 = 0.008267.
3. Finally, we can find the probability that at least one copy is received correctly by subtracting the probability that all three copies are not received correctly from 1. Thus, the probability is 1 - 0.008267 = 0.991733.
Therefore, the probability that at least one copy of the signal is received correctly is approximately 0.9917, or 99.17%.