Viruses reach networks by requests for communication that are identified as packets. A security system can detect them if at least one such packet is observed by a network sensor. Assume that the probability of observing a single packet sent from a new virus is .001. The virus actually sends 150 packets to the network computer.
What is the probability that the virus is detected by the sensor?
I feel like the answer is .001 * 150 but I am not exactly sure.
Please help
That seems right. I hope this helps. Thanks for asking.
To calculate the probability that the virus is detected by the sensor, we need to consider the probability of observing at least one packet from the virus out of the 150 packets it sends.
First, let's calculate the probability of not detecting any packet from the virus. Since the probability of observing a single packet from a new virus is 0.001, the probability of not observing a packet from the virus is 1 - 0.001 = 0.999.
To find the probability of not detecting any packet out of the 150 packets sent by the virus, we raise the probability of not detecting a single packet to the power of 150:
Prob(not detecting any packet) = (0.999)^150 ≈ 0.8688
Finally, we can find the probability of detecting at least one packet from the virus by subtracting the probability of not detecting any packet from 1:
Prob(detecting at least one packet) = 1 - 0.8688 ≈ 0.1312
Therefore, the probability that the virus is detected by the sensor is approximately 0.1312, or 13.12%.
So, your initial calculation was not correct. The correct probability calculation involves considering the probability of not detecting any packet and then subtracting that from 1 to find the probability of detecting at least one packet.