Aptitude Questions: Probability Set 8

Hello Aspirants. Welcome to Online Quantitative Aptitude Section in AffairsCloud.com. Here we are creating question sample in Probability, which is common for all the  competitive exams. We have included Some questions that are repeatedly asked in bank exams !!

  1. A box contains tickets numbered from 1 to 24. 3 tickets are to be chosen to give 3 prizes. What is the probability that at least 2 tickets contain a number which is multiple of 3? 
    A) 35/256
    B) 33/220
    C) 63/253
    D) 43/190
    E) 59/253
    Answer & Explanation
    C) 63/253
    Explanation:

    From 1 to 24, there are 8 numbers which are multiple of 3
    Case 1: 2 are multiple of 3, and one any other number from (24-8) = 16 tickets
    8C2*16C1 / 24C3 = 56/253
    Case 2: all are multiples of 3.
    8C3 / 24C3 = 7/253
    Add both cases.
  2. A box contains 6 blue, 5 green and 4 red balls. Two balls are drawn at random. What is the probability that there is no red ball?
    A) 3/30
    B) 11/21
    C) 5/18
    D) 11/23
    E) None of these
    Answer & Explanation
    B) 11/21
    Explanation:

    Total balls = 15
    Not red means green or blue i.e. any of (5+6) = 11 balls
    So prob. = 11C2 / 15C2
  3. From a pack of 52 cards, 2 cards are drawn at random. What is the probability that both cards are black card or  heart card?
    A) 31/102
    B) 21/73
    C) 1/5
    D) 17/100
    E) 3/10
    Answer & Explanation
    A) 31/102
    Explanation:

    Prob. of black card:
    26C2 / 52C2 = 25/102
    Prob. of heart card:
    13C2 / 52C2 = 3/51
    Add both cases.
  4. Two cards are drawn at random from a pack of 52 cards. What is the probability that either both are black or both are jacks?
    A) 62/221
    B) 21/312
    C) 5/21
    D) 55/221
    E) None of these
    Answer & Explanation
    D) 55/221
    Explanation:

    There are total 26 cards black, and 4 jacks in which 2 are black jacks
    So case 1: both are black
    26C2/52C2
    case 2: both are jack
    4C2/52C2
    Add both cases.
    But now 2 black jacks have been added in both cases, so subtracting their prob. : 2C2/52C2
    So 325/1326 + 6/1326 – 1/1326
  5. From a group of 3 men, 4 women and 2 children, 4 people are to be chosen to form a committee. What is the probability that the committee contains 1 each of men, women and children?
    A) 4/15
    B) 12/21
    C) 4/19
    D) 11/31
    E) None of these
    Answer & Explanation
    B) 12/21
    Explanation:

    Case 1: Prob. when 2 men, 1 woman and 1 child
    3C2*4C1*2C1 /9C4 = 4/21
    Case 2: Prob. when 1 man, 2 women and 1 child
    3C1*4C2*2C1 /9C4 = 2/7
    Case 3: Prob. when 1 man, 1 woman and 2 children
    3C1*4C1*2C2 /9C4 = 2/21
  6. A box contains 25 bulbs out of which 5 are defective. 3 bulbs are to be delivered to a customer. What is the probability that he get one defective bulb?
    A) 19/46
    B) 25/51
    C) 44/77
    D) 21/46
    E) None of these
    Answer & Explanation
    A) 19/46
    Explanation:

    5C1*20C2/25C3
  7. There are 4 red balls, 5 white and 3 green balls in a basket. 3 balls are chosen at random. What is the probability that there is at most 1 green ball?
    A) 13/40
    B) 48/55
    C) 25/68
    D) 8/33
    E) 9/19
    Answer & Explanation
    B) 48/55
    Explanation:

    Case 1: 0 green ball means all three red or white balls
    9C3/12C3
    Case 2: 1 green ball and two red or white balls
    9C2*3C1/12C3
    Add both cases.
  8. A bag contains 3 red, 4 green and 3 yellow balls. If 2 balls are drawn at random, what is the probability that they are of different color?
    A) 9/16
    B) 4/15
    C) 11/15
    D) 5/11
    E) None of these
    Answer & Explanation
    C) 11/15
    Explanation:

    This will be = 1- prob.(both are same in color)
    Prob. of both same in color = [3C2+4C2+3C2]/10C2 = 12/45
    So required prob. = 1 – 12/45
  9. There are 4 black balls and 6 white balls. 2 balls are drawn one by one without replacement. What is the probability that the balls are same in color?
    A) 9/21
    B) 8/17
    C) 5/14
    D) 7/15
    E) 9/19
    Answer & Explanation
    D) 7/15
    Explanation:

    When both black, prob. = 4/10 * 3/9
    When both white, prob. = 6/10 * 5/9
    Add both cases.
  10. A bag contains 5 red balls and 4 green balls. What is the probability that both balls are same in color?
    A) 5/11
    B) 4/9
    C) 3/13
    D) 6/17
    E) None of these
    Answer & Explanation
    B) 4/9
    Explanation:

    Case 1: both red
    5C2/9C2
    Case 2: both green
    4C2/9C2
    Add both cases