The magic formula to remember for probability questions is the following:
(# of desired outcomes)/(# of possible outcomes)
For instance, if a question asks what is the probability of rolling an even number on a six-sided die, you would count the number of desired outcomes, which in this case is even numbers: 2, 4, and 6. That is a total of 3 possibilities, so that number goes in the numerator. The number of possible outcomes is 6, since there are six different numbers (1-6) you can get when tossing a six-sided die.
Our equation will look like this:
3/6 = ½
Many of you probably knew that already. You want the tough stuff—after all this is a challenge question. Before I throw you a toughie, one quick note: getting the hard questions right on the SAT is about being able to think “on the fly”. You can’t just plug the information into some handy formula and out will come the answer. The formula above will only be of use once you’ve “cracked” the problem and figured out which number goes in the numerator and which one in the denominator.
What is the probability of rolling three six-sided fair dice so that exactly one of the three numbers rolled is prime?
The answer and explanation are in the video below. Enjoy! 🙂