Probability questions in these papers are counting questions. Almost all of them reduce to favourable outcomes over total outcomes, with the difficulty sitting entirely in the counting. Each walkthrough below states both counts before it divides, so the arithmetic is never doing work the reasoning should have done.
Download the PDF — 15 questions with answers
Free, ungated, no email. This is the probability questions with answers PDF — the same 15 questions as below, with every worked solution at the back, ready to print.
The 15 questions below are ordered the way an exam block is rather than easiest-first: two gentle openers, then a run of medium, and a hard one every sixth question — 2 of the 15 sit in the hard band. Every question is a probability.
Work each question on paper before you open its solution. The walkthrough is the method itself, step for step, so reading it first turns a practice set into a reading exercise and teaches nothing. If you are stuck on the method rather than on one question, the method guide is a better place to start than the next question: Probability: count, then divide.
Every question below was generated by the same engine that mints the ComputePrep daily timed drill, and machine-checked before it reached this page — a multiple-choice question validates its own answer against its own options at generation, and ships only with a walkthrough attached. The walkthrough is the engine's own.
What is the probability that it is red?
A bag contains 6 red and 4 blue balls.
One ball is drawn at random.
What is the probability that it is red?
A bag contains 7 red and 2 blue balls.
One ball is drawn at random.
What is the probability of drawing a face card (J, Q or K)?
One card is drawn at random from a well-shuffled pack of 52 cards.
What is the probability of drawing a red card?
One card is drawn at random from a well-shuffled pack of 52 cards.
What is the probability that the sum is exactly 5?
Two fair dice are rolled together.
What is the probability that both balls are red?
A bag contains 5 red and 4 blue balls.
Two balls are drawn at random, one after the other, without replacement.
What is the probability that it is red?
A bag contains 6 red and 6 blue balls.
One ball is drawn at random.
What is the probability that it is NOT defective?
A box contains 3 defective and 5 good bulbs.
One bulb is picked at random.
What is the probability that the sum is exactly 8?
Two fair dice are rolled together.
What is the probability of drawing a heart?
One card is drawn at random from a well-shuffled pack of 52 cards.
What is the probability of drawing a red card?
One card is drawn at random from a well-shuffled pack of 52 cards.
What is the probability of drawing a face card (J, Q or K)?
One card is drawn at random from a well-shuffled pack of 52 cards.
What is the probability that it is NOT defective?
A box contains 5 defective and 4 good bulbs.
One bulb is picked at random.
What is the probability that it is NOT defective?
A box contains 2 defective and 3 good bulbs.
One bulb is picked at random.
What is the probability that it is NOT defective?
A box contains 5 defective and 3 good bulbs.
One bulb is picked at random.
Most free practice for this topic is a scanned upload or a blog quiz, and neither can tell you a question has exactly one answer. That is the one thing this set can promise: it is minted, not typed. The engine behind it serves ComputePrep's daily timed drill, so the questions here are the same shape as the ones a live round would give you — and there is an unlimited supply of them, which is why this page can be regenerated rather than padded.
If you want the method rather than more questions, Probability: count, then divide covers the approach, the traps and a worked table. This page and that one deliberately answer different questions: that one is how do I solve these, this one is give me probability questions with the answers.
Add for "or" with mutually exclusive events; multiply for "and" with independent ones. If the events can happen together, subtract the overlap after adding. Reading the question for which connective it uses settles the method before any counting begins.
The complement. Probability of at least one equals one minus the probability of none, and "none" is a single product where "at least one" is a sum of several cases. This one substitution turns most of the harder exam probability questions into one line.
For the ball-and-bag family, combinations — order does not matter when you draw a handful. Use permutations only when the question distinguishes arrangements, such as seating or forming numbers. Choosing the wrong one changes both counts, and they often do not cancel.
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