How important is it that I study Probability if I like Analysis/Algebra much more? Is it crucial to a student's undergraduate studies in Math that he/she takes a course in Probability and/or Statistics? I am much more interested in Analysis/ Algebra and I was wondering if it would be seriously harmful if I chose not to take these courses.
 A: I have waited to reply because my field is probability and statistics, so I was afraid you'd consider my views biased. Now I would like to agree with the Comments, but with a little more detail.
For several reasons, based on my own experience and the paths
of many students I have advised over the years, I believe it is
too early for you to limit your options.
It is possible, but by no means certain, that you really know at
this point what your main interests are going to be when you
get into your graduate study. Charismatic faculty and student friends
can go a long way towards influencing your current preferences. Also,
the advanced versions of some topics may be more or less
interesting to you than the relatively introductory versions you have
seen so far.
Eventually, you will need to think what your career will be like
after you finish graduate work. Maybe you will remain in an
academic setting and maybe you won't. Either way, a field of
mathematics that is tremendously exciting during a few years
as a student may seem less interesting when you think of your
long-term career path. Some very interesting research in the
mathematical sciences is done in universities, but other types
of deep and important mathematical research are done at government agencies and
research campuses of major corporations. (I believe it is fair to say  that
some entire sub-fields of mathematics are either secret or proprietary.)
Fields of mathematics have a way of blending together in advanced
research. My own PhD thesis was technically in abstract probability theory
but about half of it was metric topology. 
A few additional examples: Group theory has also
provided important insights in probability theory and modeling.
Computer graphics and simulation have become valuable assets for visualization
in certain areas of geometry, topology, and group theory. 
Parts of cryptography and number theory are now essentially
indistinguishable. Parts of meteorology and partial differential
equations are inseparable. CERN is full of mathematicians
and statisticians. Big data analysis is in its irreverent and
exploratory 'teenage' years, and it is not yet clear what
parts of mathematics (presumably in addition to statistics) will 
eventually be useful. Brain science is becoming more mathematical
by the day, and in surprising ways.
Once again: much too early to limit your options.
A: You're an undergraduate. You don't know that you like analysis or algebra yet. Give it time. 
Everything at higher levels blends together anyway. You like analysis? In functional analysis, you will deal with measure theory. Measure theory is probability. 
