VITEEE Maths Probability Previous Year Questions

VITEEE Maths Probability PYQ, free to download as a 19-page PDF. The bank carries 14 solved questions from the 2022 to 2026 papers and takes roughly half an hour to work through, so treat it as one short revision sitting.

Questions run newest year first, with the options exactly as printed. The answer key follows, then a worked solution for each one.

VITEEE Probability Weightage

Probability is Unit 9 of the ten in VITEEE Mathematics, which is 40 of the 125 questions in the paper. It is a small unit that pays well: two or three questions a year, most of them solvable inside a minute once the right rule is spotted.

The spread is unusually even, so nothing here is a one-off. Papers up to 2025 gave one mark with no penalty; from 2026 the scheme is plus four and minus one, which makes guessing on a conditional-probability question expensive.

The three questions from 2026 ask for a value rather than a lettered option, because VIT does not release its papers.

Formulas Worth Memorising

• P(A or B) = P(A) + P(B) minus P(A and B)
• P(A given B) = P(A and B) over P(B)
• A and B are independent when P(A and B) = P(A) times P(B)
• Binomial: mean is np, variance is npq
• Population variance is the mean of the squared deviations, divided by n and not n minus one

How to Approach the Set

Any distribution carrying an unknown constant is solved the same way: the probabilities sum to one. That single equation fixes the constant, and everything the question asks follows from it.

Transfers and reinforcements look fiddly but are mechanical. Condition on the first draw, work out the probability in each of the two resulting situations, and weight them. In both such questions here the bag ends up the same size whichever colour moves, which fixes the denominator early.

And before starting any long calculation, ask whether symmetry settles it. The question about a deck with two unknown cards missing is a quarter, and no amount of casework improves on that.

Common Mistakes

• Leaving the denominator unchanged on a second draw made without replacement
• Forgetting that 2 is prime, or assuming 9 is, when counting dice sums
• Adding two overlapping card counts without subtracting the card common to both
• Dividing by n minus one when the question wants a population variance
• Reading a strict inequality as though it included its endpoints. P(0 < x < 5) covers four values, not six

Two to Solve First

The 2025 missing-cards question is the best example in the bank of symmetry doing all the work. Nothing is known about which two cards were removed, so no suit is favoured and the answer is a quarter. A full calculation over every possible pair returns the same number.

The 2026 reinforced urn is worth learning as a general fact. A ball is drawn and returned with two more of its colour, and the probability that the second ball is red comes out equal to the original fraction of red balls. That is true whatever the reinforcement.

Video Solutions

Source: Brain Blitz Audios

Using the Answer Key

Attempt all 14 before checking anything. Mark the key in one pass, right or wrong only, then go back. Each solution opens with a one-line quick solution, so you can read that much, stop, and retry before reading the full working.