# Math Help - Dicrete Probability

1. ## Dicrete Probability

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?

What I did was multiply 0.001 by 150 but I am not 100% sure it's correct. Can someone please confirm that for me.

Thanks

2. Hello, sp00ky!

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 0.001.
The virus actually sends 150 packets to the network computer.

What is the probability that the virus is detected by the sensor?
If I read all this correctly: . $P(\text{detect the virus}) \:=\:0.001$

There are 150 packets to inspect.

The probability that it detects no virus is: . $(0.999)^{150}$

Therefore, the probability that the virus is detected

. . (at least once) is: . $\boxed{1 - (0.999)^{150}}$