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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 (264 of them, from 81 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.

20% of the pool is graded hard on this site’s own scale and 25% easy, which is about average for this section.

Questions
264
Practice set
25 in 25 min
Difficulty
66/144/54
Negative marking
None
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Probability questions with solutions

6 from the 264-question pool, worked in full.

  1. 1. Two fair six-sided dice are rolled. What is the probability that their sum is 9?

    • A. 5/36
    • B. 1/12
    • C. 1/6
    • D. 1/9 ✓

    Solution. The favorable ordered pairs are (3,6),(4,5),(5,4),(6,3): 4 out of 36, giving 1/9.

  2. 2. Two fair dice are thrown. The probability that the sum is 8 is

    • A. 5/36 ✓
    • B. 1/6
    • C. 1/12
    • D. 7/36

    Solution. The outcomes summing to 8 are (2,6),(3,5),(4,4),(5,3),(6,2), giving 5 out of 36 outcomes.

  3. 3. A sensor is selected from Batch X with probability 0.7 and from Batch Y with probability 0.3. The probability that a sensor fails calibration is 0.02 for X and 0.06 for Y. Given that the selected sensor fails calibration, the probability that it came from Batch Y is

    • A. 7/16
    • B. 3/8
    • C. 9/16 ✓
    • D. 3/5

    Solution. By Bayes' theorem, P(Y|F)=0.3×0.06/(0.7×0.02+0.3×0.06)=0.018/(0.014+0.018)=18/32=9/16.

  4. 4. 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.

  5. 5. A fair die is rolled twice. What is the probability that the sum is 8?

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

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

  6. 6. Two cards are drawn together at random from a well-shuffled standard pack of 52 cards. What is the probability that both are kings?

    • A. 1/221 ✓
    • B. 2/221
    • C. 1/169
    • D. 1/13

    Solution. The number of ways of choosing two kings is C(4,2) = 6 out of C(52,2) = 1326 equally likely pairs, so the probability is 6/1326 = 1/221.

Exams that set Probability

13 categories, led by Engineering, Management, Banking.

Also set by CMAT, COMEDK UGET, CUCET, CUSAT CAT, DSSSB TGT, 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, MPPSC SSE, NATA, Navy SSR, NCHM JEE, NDA, NERIST NEE, NIFT, NIPER JEE, NMAT, NVS TGT, OPSC OCS, 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, UPPSC PCS, UPSC ISS, Uttarakhand JEEP, VITEEE, VTUEEE, WB JELET, WBJEE, XAT, JAMB UTME. Browse all exams.

Probability: frequently asked questions

How many probability questions are there?

264, from the 81 exams here whose syllabus sets the topic. 25% are graded easy and 20% hard, which makes probability about average for this section, where the mean is 17%.

Which exams ask probability questions?

81 of the exams on this site, weighted towards Engineering (41), Management (10), 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?

20% of these 264 questions are graded hard and 25% easy, making it about average for this section, where the mean is 17%.

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