By Thabane L.

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**Extra info for A closer look at the distribution of number needed to treat (NNT) a Bayesian approach (2003)(en)(6s)**

**Sample text**

We choose an integer N at random from {1, 2, . . , 103 }. What is the probability that N is divisible by 3? by 5? by 105? How would your answer change if 103 is replaced by 10k , as k gets larger and larger? 13. Consider the complete graph K4 with four vertices; all vertices are connected by an edge to all other vertices. Suppose now that we ﬂip an unbiased coin for each edge. If heads comes up, we leave the edge where it is, if tails comes up we remove the edge. (a) What is the probability that two given vertices are still connected after the removal of the edges?

We can now, with this information, compute the probability that John Smith is the murderer, given the event that his DNA proﬁle was found at the scene of the crime, that is, we can compute P (G|E): P (G|E) = = = P (E|G)P (G) P (E|G)P (G) + P (E|Gc )P (Gc ) 1/(n + 1) 1/(n + 1) + (pn)/(n + 1) 1 . 1 + pn This is alarming, since the two methods give diﬀerent answers. Which one is correct? We will now explain why method (1) is wrong. 2). This seems obvious, but is, in fact, not correct. The fact that the ﬁrst person to be checked has the particular DNA proﬁle, says something about the total number of individuals with this proﬁle.

What would be the fair ‘entry fee’ for this game? In other words, how much money would you be willing to pay in order to play this game? Perhaps you want to base this amount on the expectation of X. The idea would be that the expectation of X is the average amount of money that you recieve, and it would be only fair to pay exactly this amount in advance, making the game fair. However, we have ∞ 2n 2−n = ∞, E(X) = n=1 and you would not be willing (or able) to pay an inﬁnite amount of money to play this game.