Today’s SAT question of the day is an excellent review of probability.  You will probably encounter 2-3 probability questions on your SAT, so take advantage of these points if you can.

The question:

Of 5 employees, 3 are to be assigned an office and 2 are to be assigned a cubicle. If  3 of the employees are men and 2 are women, and if those assigned an office are to be chosen at random, what is the probability that the offices will be assigned to 2 of the men and 1 of the women?

Where to start? As with all probability problems, we need to find the number of total possible outcomes and the number of desired outcomes so that we can get our fraction of desired/possible.

At the beginning of our selection process, we have a total of 5 workers.  Imagine that our workers are named A, B, C, D, and E. How many unique three-person combinations can we make out of A, B, C, D, and E?  Let’s check:

ABC
ABD
ABE
ACD
ACE
ADE
BCD
BCE
BDE
CDE

Ten groupings it is. So, we have 10 possible outcomes.Now to figure out the desired outcomes.  There are 3 men from which to choose and 2 women. 3 x 2 = 6 groupings of two men and one woman.  Confused by the math behind that idea? Imagine that A, B, and C are the men and D and E are the women.  Go back to the list of combinations and count how many leave us with 2 men and one woman – you’ll get 6 that way, too!

Putting desired/possible, we get 6/10 or 3/5.  This one had a few steps to it, but it’s a great review opportunity for your test day! It can seem like writing out these combinations will take too much time, but you will probably find that you can get to your answer more quickly than you had imagined since you’re not trying to remember what you’re supposed to do with the sigma and when….