GMAT probability strategies

GMAT probability tests whether you know when to multiply and when to add. These strategies cover the core formula, the complement rule for "at least" questions, the trap of adding when you should multiply, and a worked example you can follow step by step.

The core formula

The probability of an event is the number of favorable outcomes divided by the total number of possible outcomes: $P = \frac{\text{favorable}}{\text{total}}$ . A fair six-sided die has 6 total outcomes. The probability of rolling a 4 is $\frac{1}{6}$ . The probability of rolling an even number is $\frac{3}{6} = \frac{1}{2}$ , because 3 of the 6 outcomes are even. Every probability question starts from this ratio. The total must cover every possible outcome, and the favorable must be a subset of it.

The complement rule for "at least" questions

When a question asks for the probability of 'at least one' success, computing it directly means summing one success, two successes, three successes, and so on. The complement rule is faster: $P(\text{at least one}) = 1 - P(\text{none})$ . If the probability of a miss on each try is 0.3 and there are 4 tries, the probability of missing all 4 is $0.3^4 = 0.0081$ . The probability of at least one hit is $1 - 0.0081 = 0.9919$ . One subtraction replaces an entire series of additions.

The most common trap

Adding probabilities when you should multiply (or the reverse)

You need the probability of rolling a 6 on the first die AND a 6 on the second die. You add $\frac16 + \frac16 = \frac26$. The correct answer is $\frac16 \times \frac16 = \frac136$. Adding is for "or" (either event happens), multiplying is for "and" (both happen). The answer choices include $\frac26$ because the test writers know this mistake. Ask "and or or?" before you pick an operation.

Step-by-step strategy

When to use: any question that asks for a probability, a chance, or a likelihood.

1Ask: is this "and" or "or"? Multiply for "and" (both events happen). Add for "or" (either event happens), but only if the events are mutually exclusive.
2Count the favorable outcomes and the total outcomes, then divide.
3For "at least" questions, use the complement rule: compute the probability of zero successes and subtract from 1.
4Verify the result is between 0 and 1. A probability outside that range means a counting error.

When not to use: when the question asks for a count of arrangements rather than a probability (use combinatorics instead).

Worked example

A bag contains 4 red marbles and 6 blue marbles. If 2 marbles are drawn without replacement, what is the probability that both are red? Step 1: Ask 'and or or?' Both must be red, so this is 'and.' We multiply. Step 2: First draw. There are 4 red out of 10 total, so $P(\text{first red}) = \frac{4}{10} = \frac{2}{5}$ . Step 3: Second draw (without replacement). After one red is removed, 3 red and 6 blue remain, 9 total. $P(\text{second red} | \text{first red}) = \frac{3}{9} = \frac{1}{3}$ . Step 4: Multiply. $\frac{2}{5} \times \frac{1}{3} = \frac{2}{15}$ . The answer is $\frac{2}{15}$ .

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