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Math Help - Dicrete Probability

  1. #1
    sp00ky
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    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
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  2. #2
    Super Member

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    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}}

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