Question

A student will keep scanning radio stations until he finds one playing a song he likes. Assume that
the songs played on each station are independent of the others. For each station, there is a 30%
chance that the station will play a song that the student likes. Let X be the number of stations that
the student listens to (with songs he doesn’t like) until he finds one with a song that he likes. Note
that X is a geometric random variable.
a) (1) Determine the probability that the student listens to exactly 3 radio stations before the one
with a song he likes.
b) (2) Determine the probability that it takes more than 3 stations with songs he doesn’t like before
the one with a song that he likes. Hint: use the complement rule.
c) (1) Determine E(X).

Answer 1