Designing Large Scale Lans

Appendix A. Appendix: Combining Probabilities

Start with one flip of a coin. If you flip the coin once, you know the answer. Call the probability of getting heads P, so the probability of getting tails is (1-P). The symbol kPn represents the probability of getting k heads in n flips.

Flip the coin a second time. Now there are several possibilities. You could have two tails, two heads, a head and a tail, or a tail and a head. I wrote down the probabilities for one flip. The probabilities for the second flip are the same, but I have to multiply the first flip by the second. The probability of getting two heads in a row is the probability of getting heads on the first toss times the probability of getting heads on the second toss:

The most interesting example is the ₁ P ₂. It says that the probability of getting one head in two tosses is the probability of getting a head then a tail, plus a tail then a head. Substituting in the values for ₀ P ₁ and ₁ P ₁ from the previous example ...