Quantitative practice
Probability Questions with Answers
Favourable over total outcomes, dependent and independent events, and conditional probability. This page pools every probability question on the site (226 of them, from 72 exams, weighted towards Engineering, Management, Banking) so you can drill the topic on its own instead of meeting four of them inside a full paper.
21% of the pool is graded hard on this site’s own scale and 23% easy, which is about average for this section.
- Questions
- 226
- Practice set
- 25 in 25 min
- Difficulty
- 53/126/47
- Negative marking
- None
Probability questions with solutions
6 from the 226-question pool, worked in full.
1. A card drawn from a standard 52-card deck is known to be a face card. What is the probability that it is a king?
- A. 1/4
- B. 1/13
- C. 1/3 ✓
- D. 4/13
Solution. There are 12 face cards: 4 jacks, 4 queens, and 4 kings. Given that the card is a face card, the probability of a king is 4/12=1/3.
2. A fair die is rolled once. What is the probability of obtaining an even number?
- A. 1/2 ✓
- B. 1/6
- C. 1/3
- D. 2/3
Solution. Even numbers on a die are 2, 4, and 6, giving 3 favourable outcomes out of 6, which simplifies to 1/2.
3. The digits 1, 2, 3 and 4 are arranged at random to form a four-digit number, using each digit once. What is the probability that the number is divisible by 4?
- A. 1/6
- B. 1/3
- C. 1/2
- D. 1/4 ✓
Solution. Divisibility by 4 depends on the last two digits. Valid endings using distinct digits from the set are 12, 24 and 32. For each ending, the remaining two digits can be ordered in 2 ways, giving 6 favourable numbers out of 4! = 24. The probability is 1/4.
4. A bag has 4 red and 5 blue balls. Two balls are drawn without replacement. The probability both are red is
- A. 1/6 ✓
- B. 4/9
- C. 2/9
- D. 5/18
Solution. The probability is C(4,2)/C(9,2)=6/36=1/6.
5. A card is drawn from a well-shuffled deck of 52 cards. The probability that it is a king or a queen is
- A. 1/13
- B. 4/13
- C. 1/26
- D. 2/13 ✓
Solution. There are 4 kings and 4 queens, 8 favourable cards out of 52: probability = 8/52 = 2/13.
6. A bag has 5 red and 3 blue balls. Two balls are drawn without replacement. What is the probability that both are red?
- A. 5/8
- B. 15/28
- C. 5/14 ✓
- D. 3/14
Solution. P(both red)=(5/8)(4/7)=20/56=5/14.
Exams that set Probability
11 categories, led by Engineering, Management, Banking.
Drawn from Agniveer Vayu, AIIMS NORCET, AP EAPCET, AP POLYCET, Assam CEE, ATIT, ATMA, BCECE, Bihar DCECE, BITSAT, CG PET, CG PPT, CMAT, COMEDK UGET, CUCET, CUSAT CAT, GMAT, GRE, GUJCET, HP PAT, IBPS Clerk, IBPS PO, IBPS RRB Office Assistant, IBPS RRB Officer Scale I, IBSAT, IEMJEE, IMU-CET, IPMAT Indore, IPMAT Rohtak, JAIN JET, JCECE, JEE Advanced, JEE Main, JEECUP, JIPMAT, KCET, KEAM, Kerala MCA, KIITEE, KLEEE, LPUNEST, MAH MBA CET, MAH MCA CET, MHT CET, MIT-WPU CET, NATA, Navy SSR, NCHM JEE, NDA, NERIST NEE, NIFT, NIPER JEE, RBI Assistant, RRB Technician, SAT, SBI Clerk, SBI PO, SITEEE, SNAP, SRMJEEE, SSC CGL, SSC Selection Post, TG EAPCET, TG LAWCET, TG POLYCET, TJEE, UPESEAT, Uttarakhand JEEP, VITEEE, VTUEEE, WB JELET, WBJEE.
Probability: frequently asked questions
How many probability questions are there?
226, from the 72 exams here whose syllabus sets the topic. 23% are graded easy and 21% hard, which makes probability about average for this section, where the mean is 18%.
Which exams ask probability questions?
72 of the exams on this site, weighted towards Engineering (41), Management (8), Banking (7). Every question in this pool comes from one of their own mock tests, so the list below is the honest answer to whether the topic is worth your time.
Is probability hard?
21% of these 226 questions are graded hard and 23% easy, making it about average for this section, where the mean is 18%.
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