Probability on the GMAT tests your logical reasoning and systematic decision-making rather than abstract theorems. From the foundational fraction (Favorable / Total) and the 1 - P(None) complement shortcut, to independent vs. dependent events and Data Sufficiency strategy, this guided path will teach you to solve probability problems with speed and precision.
Understand the 0 to 1 probability scale, convert between fractions and percentages, and master single-event outcome calculations.
Probability measures the likelihood of an event occurring, expressed as a fraction, decimal, or percentage between 0 (impossible) and 1 (certain).
e.g., Rolling a 7 on a standard 6-sided die.
e.g., Tossing Heads on a fair coin.
e.g., Rolling a number ≤ 6 on a 6-sided die.
Learn how the complement rule turns multi-case 'at least one' problems into a 5-second calculation using 1 - P(None).
The probability of an event happening plus the probability of it NOT happening always sums to 1 (100%).
Master the difference between independent events (with replacement) and dependent events (without replacement) with interactive step-by-step models.
When the outcome of the first draw does NOT change the total or composition for the second draw (e.g. with replacement), events are independent.
Marble Draw With Replacement
A bag contains 4 Red and 6 Blue marbles (Total = 10).
A marble is drawn, its color recorded, and replaced back into the bag. A second marble is then drawn.
What is the probability that both marbles are Red?
There are 4 Red marbles out of 10 total marbles:
Because the marble was replaced, the bag still contains 4 Red and 10 total marbles:
Multiply the independent probabilities:
Understand mutually exclusive vs. overlapping events, and learn how to use Venn inclusion-exclusion logic to avoid double-counting.
If two events cannot occur at the same time ($P(A \text{ and } B) = 0$), simply add their individual probabilities.
What is the probability of drawing a King OR a Queen from a standard 52-card deck?
A card cannot be both a King and a Queen → Mutually Exclusive.
P(King) = 4/52, P(Queen) = 4/52
$$ P(\text{King or Queen}) = \frac{4}{52} + \frac{4}{52} = \frac{8}{52} = \mathbf{\frac{2}{13}} $$
Connect Permutations & Combinations (nCr) to group selection probabilities, with a direct link to our P&C guide for a full refresher.
When selecting multiple items simultaneously from a group, calculating probability involves counting combinations for both the numerator (favorable groups) and denominator (total possible groups):
Mastering the Slot Method and nCr calculation shortcuts makes probability questions much faster and error-free.
Learn to spot sufficiency from component ratios without needing total counts, and evaluate independence in Data Sufficiency questions.
On GMAT Data Sufficiency, knowing the ratio of parts is sufficient to find probability without ever knowing the actual total number of items.
Marble Jar Probability
A jar contains only red, blue, and green marbles. If one marble is drawn at random, what is the probability that the marble is red?
(1) The ratio of red to blue to green marbles is 3 : 4 : 5.
(2) The jar contains 24 blue marbles.
Target probability is the fractional share of Red marbles:
Rephrase: We only need the fractional proportion of red marbles, NOT the exact count of marbles.
Statement (1) provides the exact component ratio: 3 : 4 : 5.
Total parts = 3 + 4 + 5 = 12 parts.
A unique probability (1/4) is determined → SUFFICIENT.
Statement (2) tells us there are 24 blue marbles.
We have no information about how many red or green marbles are in the jar, nor the total count.
Cannot calculate P(Red) → INSUFFICIENT.
Final Answer: (A)
A dedicated question set for Probability is currently being authored. In the meantime, test your baseline score on the full Diagnostic:
Don't just solve questions sequentially. Learn the error log method and how to use the OG for maximum score gains.
Stop calculating! Learn how to use the properties of symmetry to solve hard SD questions in seconds.
Stop calculating sums! Learn the 'Average of First & Last' rule to solve Arithmetic Progression (AP) problems in seconds.