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Probability

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An ISP has a link of 100Mbps which is shared by its subscribers. Considering the fact that all of its subscribers are active 50% of the time and the probabilities of being active are independent, the ISP has promised 25 Mbps to its 6 subscribers. What is the probability that any subscriber gets degraded service (less than promised speed).
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The above question is an example of Binomial Experiment. Any user can be either Online(O) or Offline(F) P(O) = \frac{1}{2} P(F) = \frac{1}{2} Let X be the Random Variable denoting the number of users online. The users get degraded service when X=5 or X=6,

= P(X>4) \\ = P(X=5) + P(X=6) \\ = C(6,5) * P(O)^5 * P(F)^1 + C(6,6) * P(O)^6\\ = 6 * \frac{1}{2}^5 * \frac{1}{2}^1 + 1 * \frac{1}{2}^6\\ = \frac{7}{2^6}\\ = 7/64

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