Probability on the CAT tests analytical precision rather than mechanical formula memorization. From the foundational fraction (Favorable / Total) and the 1 - P(None) complement shortcut, to independent vs. dependent events, combinatorics, and conditional Bayes' logic, this guided path builds the first-principles fluency needed to ace CAT probability questions.
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.
Master reduced sample space techniques and reverse path probability for two-stage selection problems.
When given a condition ('Given that...'), do not use the original full sample space. Shrink the denominator to only the outcomes satisfying the condition.
Two fair 6-sided dice are rolled simultaneously.
Given that the sum of the two numbers is 8, what is the probability that at least one of the dice shows a 3?
Ignore the usual 36 outcomes ($6 \times 6$). List only the pairs whose sum is 8:
Total eligible outcomes = 5.
Within this reduced set of 5 outcomes, identify those with at least one 3:
Shrinking the denominator avoids cumbersome formula substitutions.
A dedicated question set for Probability is currently being authored. In the meantime, test your baseline score on the full Diagnostic:
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