Packet Transmission 

A packet consisting of a string of symbols is transmitted over a noisy channel. Each symbol has a probability 0.0001 of being transmitted in error. Find the largest for which the probability of incorrect transmission (at least one symbol in error) is less than 0.001.

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X transmissionProcess = BinomialProcess[10^-4];

The probability of an error in the transmission.

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X prob = Probability[x > 0, x \[Distributed] transmissionProcess[n]]

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X ListLogPlot[Transpose@Table[{prob, 10^(-3)}, {n, 0, 15}], Joined -> True, Filling -> Axis]

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Find the largest for which the probability of incorrect transmission is less than .

In[4]:=

X Maximize[{n, prob <= 10^-3 && n \[Element] Integers && 5 <= n <= 15}, n]

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