4.14 SAT Math - Probability

Probability questions are really just another type of ratio or proportion problem.  Put the number you're concerned about on top, and the total outcomes on the bottom of your fraction.

6. A bag contains ten red marbles, 12 blue, 15 yellow, and 8 white marbles.  If one marble is pulled from the bag at random, what is the probability that it will be red?
We care about the red marbles, so ten goes on top of our fraction.  What's the total possible outcomes?  To find that, add up all the pieces: 10+12+15+8=45.  So our probability is 10/45 which can be simplified to 2/9.

More complicated probability questions on the SAT math section will ask you to find the probability of two or more events.  To solve these, you must decide if the events are independent of each other or dependent on each other.  Independent events are events in which one outcome does not affect the other.  Things like a coin flip, a roll of a die a second time, or the bag of marbles if the first marble is put back into the bag are all independent events.  To solve independent events probabilities, just multiply together each individual probability:

If an identical coin is flipped under identical circumstances, what is the probability of flipping heads four times in a row?

The probability of flipping heads is 1/2.  That probability doesn't change just because of circumstances, so to find the answer to the question, simply multiply 1/2 by itself 4 times: 1/2 • 1/2 • 1/2 • 1/2 or 1/16. 

A dependent event's results will change based on the results of the first event.  Take this example:
Sara has four $10 bills, three $20 bills, and five $5 bills.  If she draws two bills at random, what is the probability that she has drawn one twenty-dollar bill and one five?
The probability of her first bill is an independent event, so we'll set up our fraction as  or 3/12.  The probability of pulling a five-dollar bill as the second draw, however, is different.  There is now one less bill in the wallet, so the probability of pulling a five is now 5/11.  The probability of pulling them both together is the product of those two answers, or 3/12 • 5/11.  Multiplying those together gives us an answer of 5/44.