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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 — 213 of them, from 70 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.

17% of the pool is graded hard on this site’s own scale and 25% easy, which is about average for this section.

Questions
213
Practice set
25 in 25 min
Difficulty
53/123/37
Negative marking
None
Start Probability practice

Probability questions with solutions

6 from the 213-question pool, worked in full.

  1. 1. A bag has 5 orange, 4 white and 3 black counters. The probability of drawing a white counter is:

    • A. 1/4
    • B. 1/3 ✓
    • C. 3/8
    • D. 4/9
    • E. 2/3

    Solution. There are 12 counters; 4 are white, so 4/12=1/3.

  2. 2. Two fair coins are tossed and one fair six-sided die is rolled. What is the probability that the die shows a number exactly one more than the number of heads obtained?

    • A. 1/6 ✓
    • B. 1/4
    • C. 1/3
    • D. 1/2

    Solution. There are 4 equally likely coin outcomes and 6 die outcomes, giving 24 equally likely combined outcomes. For TT the die must show 1; for HT and TH it must show 2; for HH it must show 3. Thus there are 4 favourable outcomes, so the probability is 4/24=1/6.

  3. 3. Two fair dice are thrown. What is the probability that the sum is 8?

    • A. 5/36 ✓
    • B. 7/36
    • C. 1/9
    • D. 1/6

    Solution. The favourable ordered pairs are (2,6), (3,5), (4,4), (5,3), (6,2): 5 out of 36.

  4. 4. A positive divisor of 360 is selected uniformly at random. What is the probability that it is divisible by 12?

    • A. 1/4
    • B. 1/2
    • C. 1/3 ✓
    • D. 2/3

    Solution. Since 360 = 2^3 x 3^2 x 5, it has (4)(3)(2) = 24 positive divisors. A divisor divisible by 12 = 2^2 x 3 must have exponent of 2 equal to 2 or 3, exponent of 3 equal to 1 or 2, and exponent of 5 equal to 0 or 1: 2 x 2 x 2 = 8 divisors. Thus the probability is 8/24 = 1/3.

  5. 5. One card is drawn from a standard deck of 52 cards. What is the probability that it is a face card?

    • A. 4/13
    • B. 3/13 ✓
    • C. 1/13
    • D. 9/52

    Solution. There are 12 face cards, so probability=12/52=3/13.

  6. 6. A box contains 4 red, 5 blue and 3 green tokens. One token is drawn at random. The probability it is not blue is:

    • A. 5/12
    • B. 1/2
    • C. 2/3
    • D. 7/12 ✓
    • E. 7/10

    Solution. There are 12 tokens, 7 of which are not blue.

Exams that set Probability

11 categories, led by Engineering, Management, Banking.

Also set by 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, VTUEEE, WB JELET, WBJEE. Browse all exams.

Probability: frequently asked questions

How many probability questions are there?

213, from the 70 exams here whose syllabus sets the topic. 25% are graded easy and 17% hard, which makes probability about average for this section, where the mean is 17%.

Which exams ask probability questions?

70 of the exams on this site, weighted towards Engineering (40), 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?

17% of these 213 questions are graded hard and 25% easy, making it about average for this section, where the mean is 17%.

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