Probability problems come up quite a bit on the GMAT, so it is important to understand them. The Probability of an event is:
# of Successful outcomes
# of Total possible outcomes
Say, for instance we want to calculate the probability that you roll three on a six-sided die. The number of successful outcomes is 1, because there is only one three on the die. The total number of possible outcomes is 6, because there are 6 sides to the die. So the probability of rolling a three is 1/6. On the other hand, if you wanted to know the probability that you will roll an even number, you have three successful outcomes (2,4,6). This means the probability is 3/6 or ½.
If you want to know the probability of one or more event together, you need to know if it is an “or” combination or and “and” combination. For example, the probability of rolling a 6 or a 2, is very different than the probability of rolling a 6 and then a 2.
Whenever you have events connected by an “or,” you add the probability of the two events. For example, if you want to know that probability of rolling a 6 or a 2, you take the probability of getting a 6 (1/6) and add it to the probability of getting a 2 (1/6), making the total probability 2/6 or 1/3.
When you have events connected by an “and” or an “and then,” you need to multiply the two probabilities. This is because you need each of the events to happen, which makes it that much less probable. So, the probability of rolling a 6 and then a 2, is (1/6)(1/6)= 1/36.
When you have events combined with “and,” its important to understand if the events are connected, which means that one event affects the probability of another event. When you roll a die or flip a coin, whatever you flipped the last time won’t affect the probability of the next flip or roll.
When you have a deck of cards, however, and you remove cards one after the other, the card you pull out affects the probability of future events. For example, if you have a full deck the probability that you will pull out a red card is ½. If you pull out an ace of hearts, the probability that you will then pull out a red card is 25/51, because you are removing one of the total possibilities and one successful probability.