Home / General Aptitude / Probability

15 Probability Questions and Answers

15 solved Probability questions with step-by-step explanations. Includes formulas, shortcuts, and tips for placement tests and competitive exams.

Probability measures the likelihood of an event occurring, expressed as a number between 0 (impossible) and 1 (certain). In aptitude tests, probability questions typically involve dice rolls, card draws from a standard deck of 52 cards, coin tosses, or selection from a group of items. The basic formula is P(Event) = Number of favorable outcomes ÷ Total number of possible outcomes. Key concepts include independent events (the outcome of one does not affect another), mutually exclusive events, and conditional probability. Below are solved probability questions covering these essential patterns.

Q1 Easy

A fair die is rolled once. What is the probability of getting a prime number?

  • A. 1/6
  • B. 4/6
  • C. 2/6
  • D. 3/6
Explanation: Prime outcomes are 2, 3, 5 (3 outcomes) out of 6. Probability = 3/6 = 1/2.
Q2 Easy

A fair die is rolled once. Probability of getting a number greater than 3?

  • A. 3/6 (1)
  • B. 4/6
  • C. 2/6
  • D. 3/6
Explanation: Numbers greater than 3: 3 outcomes out of 6. Probability = 3/6.
Q3 Easy

From a standard 52-card deck, what is the probability of drawing a black card?

  • A. 12/52
  • B. 26/52
  • C. 13/52
  • D. 39/52
Explanation: Black suits are spades and clubs: 13 + 13 = 26 cards. Probability = 26/52 = 1/2.
Q4 Easy

A bag has 6 red and 5 blue balls. Probability of picking a red ball?

  • A. 6/5
  • B. 5/11
  • C. 6/11
  • D. 11/6
Explanation: Favorable outcomes = 6, total outcomes = 11. So probability = 6/11.
Q5 Easy

A fair die is rolled once. What is the probability of getting an even number?

  • A. 2/6
  • B. 4/6
  • C. 3/6
  • D. 1/6
Explanation: Even outcomes are 2, 4, 6 (3 outcomes) out of 6. Probability = 3/6 = 1/2.
Q6 Easy

A bag has 1 red and 5 blue balls. Probability of picking a red ball?

  • A. 6/1
  • B. 1/6
  • C. 5/6
  • D. 1/5
Explanation: Favorable outcomes = 1, total outcomes = 6. So probability = 1/6.
Q7 Medium

From a standard 52-card deck, what is the probability of drawing a Club?

  • A. 1/2
  • B. 26/52
  • C. 1/4
  • D. 13/52
Explanation: There are 13 clubs in 52 cards. Probability = 13/52 = 1/4.
Q8 Medium

A bag has 6 red and 8 blue balls. Probability of picking a red ball?

  • A. 6/8
  • B. 8/14
  • C. 14/6
  • D. 6/14
Explanation: Favorable outcomes = 6, total outcomes = 14. So probability = 6/14.
Q9 Medium

From a 52-card deck, what is the probability of drawing a face card (J, Q, or K)?

  • A. 12/52
  • B. 16/52
  • C. 13/52
  • D. 10/52
Explanation: Each suit has J, Q, K so face cards = 3 x 4 = 12. Probability = 12/52 = 3/13.
Q10 Medium

A bag has 1 red and 7 blue balls. Probability of picking a red ball?

  • A. 8/1
  • B. 1/8
  • C. 7/8
  • D. 1/7
Explanation: Favorable outcomes = 1, total outcomes = 8. So probability = 1/8.
Q11 Medium

From a standard 52-card deck, what is the probability of drawing a red card?

  • A. 26/52
  • B. 39/52
  • C. 13/52
  • D. 12/52
Explanation: Red suits are hearts and diamonds: 13 + 13 = 26 cards. Probability = 26/52 = 1/2.
Q12 Hard

A bag has 5 red and 7 blue balls. Probability of picking a red ball?

  • A. 7/12
  • B. 12/5
  • C. 5/12
  • D. 5/7
Explanation: Favorable outcomes = 5, total outcomes = 12. So probability = 5/12.
Q13 Hard

From a standard 52-card deck, what is the probability of drawing a Diamond?

  • A. 13/52
  • B. 26/52
  • C. 1/4
  • D. 1/2
Explanation: There are 13 diamonds in 52 cards. Probability = 13/52 = 1/4.
Q14 Hard

A bag has 3 red and 2 blue balls. Probability of picking a red ball?

  • A. 3/2
  • B. 5/3
  • C. 2/5
  • D. 3/5
Explanation: Favorable outcomes = 3, total outcomes = 5. So probability = 3/5.
Q15 Hard

A fair die is rolled once. Probability of getting a number greater than 4?

  • A. 2/6
  • B. 3/6
  • C. 1/6
  • D. 4/6
Explanation: Numbers greater than 4: 2 outcomes out of 6. Probability = 2/6.

Key Takeaways

  • Total outcomes for N coin tosses = 2^N. For N dice = 6^N.
  • Cards: 52 total = 4 suits × 13 ranks. Know the composition of the deck.
  • For 'or' events: P(A or B) = P(A) + P(B) - P(A and B).

Frequently Asked Questions

What is the basic formula for probability?

Probability = Number of favorable outcomes ÷ Total number of possible outcomes. Always express as a fraction, decimal, or percentage between 0 and 1.

What are independent and mutually exclusive events?

Independent: Outcome of one does NOT affect the other (e.g., rolling dice twice). P(A and B) = P(A) × P(B). Mutually exclusive: Events cannot occur together (e.g., getting heads and tails on one coin toss). P(A or B) = P(A) + P(B).

More Probability Practice Resources

For more probability practice, try our timed quiz mode that generates fresh questions every session.