5
$\begingroup$

You are trying to locate an old high school friend who lives in Chicago. Unfortunately, your friend's name is Anthony Smith and the Chicago phone book lists phone numbers for $24$ different people named Anthony Smith. (Assume that your friend's phone number is listed in the phone book, and that you don't call anybody twice.)

Let $X$ be the number of calls you need to make until you find your friend. Give the probability mass function for $X$.

I think $X$ will have a Geometric distribution? but with what $p$?? Also, as I know in the geometric distribution the number of trials could be infinity, but here we have at most $24$?

  • 0
    I would be a geometric if, after each unsucessfull attempt, you forget about it, and peak again at random one of the 24 numbers. Not your case (" you don't call anybody twice"). See comments above. After you solve it, it's interesting to compare with the geometric.2011-09-20

1 Answers 1

2

Just to get an answer on record ...

HINT: Imagine that you call the Anthony Smiths in the order in which they’re listed in the phone book (until you reach your friend). Is your friend more likely to be third in the list than $23$rd, or $17$th? More generally, is your friend any more likely to be in one position in that list than in another?