**Long time, no blog**

Life's been keeping me busy. I'll post an update soon. Briefly: finished my summer job for the Amalgamated Insight (née TelegraphCQ) folks. I'm now back at Queen's for the last year of my undergrad.

**Interesting math**

An assignment in one of my classes included an interesting bonus problem. It is very simple, but I confess I got it completely wrong before I saw the solution. Maybe one of you bright folks is smarter than I:

Let the alphabetA= {a, b, c, ..., z} (Ais the set of 26 lowercase letters of the English alphabet). LetS1(w)be true iff the stringwover alphabetAcontains the substringaaa; letS2(w)be true iff the stringwcontains the substringabc.

Suppose we choose a

wof 10 characters; each character inwis selected randomly and independently.

Let

P1be the probability thatS1(w)is true, and letP2be the probability thatS2(w)is true. IsP1 > P2,P1 < P2, orP1 = P2? Give a justification for your answer. (Hint:P1 != P2).

If you think you know the answer,
email me
—
I'll post
the answer later (`neilc A T samurai D O T com`).
Obviously, the gist is in the
justification, not which alternative you think is true.

Hat Tip: Prof. Kai Salomaa for showing me the problem.