Quantitative Aptitude: Probability Set 1

Shubhra
  1. From a pack of 52 cards, 1 card is chosen at random. What is the probability of the card being diamond or queen?
    A) 2/7
    B) 6/15
    C) 4/13
    D) 1/8
    E) 17/52
    View Answer
    Option C
    Solution:
    In 52 cards, there are 13 diamond cards and 4 queens.
    1 card is chosen at random
    For 1 diamond card, probability = 13/52
    For 1 queen, probability = 4/52
    For cards which are both diamond and queen, probability = 1/52
    So required probability = 13/52 + 4/52 – 1/52 = 16/52 = 4/13
  2. From a pack of 52 cards, 1 card is drawn at random. What is the probability of the card being red or ace?
    A) 5/18
    B) 7/13
    C) 15/26
    D) 9/13
    E) 17/26
    View Answer
    Option B
    Solution:
    In 52 cards, there are 26 red cards and 4 ace and there 2 such cards which are both red and ace.
    1 card is chosen at random
    For 1 red card, probability = 26/52
    For 1 ace, probability = 4/52
    For cards which are both red and ace, probability = 2/52
    So required probability = 26/52 + 4/52 – 2/52 = 28/52 = 7/13
  3. There are 250 tickets in an urn numbered 1 to 250. One ticket is chosen at random. What is the probability of it being a number containing a multiple of 3 or 8?
    A) 52/125
    B) 53/250
    C) 67/125
    D) 101/250
    E) 13/25
    View Answer
    Option A
    Solution:
    Multiples of 3 up to 250 = 250/3 = 83 (take only whole number before the decimal part)
    Multiples of 8 up to 250 = 250/3 = 31
    Multiples of 24 (3×8) up to 250 = 250/24 = 10
    So total such numbers are = 83 + 31 – 10 = 104
    So required probability = 104/250 = 52/125
  4. There are 4 white balls, 5 blue balls and 3 green balls in a box. 2 balls are chosen at random. What is the probability of both balls being non-blue?
    A) 23/66
    B) 5/18
    C) 8/21
    D) 7/22
    E) 1/3
    View Answer
    Option D
    Solution:
    Both balls being non-blue means both balls are either white or green
    There are total 12 balls (4+3+5)
    and total 7 white + green balls.
    So required probability = 7C2/12C2 = [(7*6/2*1) / (12*11/2*1)] = 21/66 = 7/22
  5. There are 4 white balls, 3 blue balls and 5 green balls in a box. 2 balls are chosen at random. What is the probability that first ball is green and second ball is white or green in color?
    A) 1/3
    B) 5/18
    C) 1/2
    D) 4/21
    E) 11/18
    View Answer
    Option B
    Solution:
    There are total 4+3+5 = 12 balls
    Probability of first ball being green is = 5/12
    Now total green balls in box = 5 – 1 = 4
    So total white + green balls = 4 + 4 = 8
    So probability of second ball being white or green is 8/12 = 2/3
    So required probability = 5/12 * 2/3 = 5/18
  6. 2 dices are thrown. What is the probability that there is a total of 7 on the dices?
    A) 1/3
    B) 2/7
    C) 1/6
    D) 5/36
    E) 7/36
    View Answer
    Option C
    Solution:
    There are 36 total events which can happen ({1,1), {1,2}……………….{6,6})
    For a total of 7 on dices, we have – {1,6}, {6,1}, {2,5}, {5,2}, {3,4}, {4,3} – so 6 choices
    So required probability = 6/36 = 1/6
  7. 2 dices are thrown. What is the probability that sum of numbers on the two dices is a multiple of 5?
    A) 5/6
    B) 5/36
    C) 1/9
    D) 1/6
    E) 7/36
    View Answer
    Option E
    Solution:
    There are 36 total events which can happen ({1,1), {1,2}……………….{6,6})
    For sum of number to be a multiple of 5, we have – {1,4}, {4,1}, {2,3}, {3,2}, {4,6}, {6,4}, {5,5} – so 7 choices
    So required probability = 7/36
  8. There are 25 tickets in a box numbered 1 to 25. 2 tickets are drawn at random. What is the probability of the first ticket being a multiple of 5 and second ticket being a multiple of 3.
    A) 5/11
    B) 1/4
    C) 2/11
    D) 1/8
    E) 3/14
    View Answer
    Option D
    Solution:
    There are 5 tickets which contain a multiple of 5
    So probability of 1st ticket containing multiple of 5 = 5/25 = 1/5
    Now:
    Case 1: If the ticket chosen contained 15
    If there was a 15 on first draw, then there are 7 tickets in box which contain a multiple of 3 out of 24 tickets. (25/3 – 1 = 8 – 1 = 7) – because 15 is already out from the box
    So probability = 7/24 (24 tickets remaining after 1st draw)
    Case 2: If the ticket chosen contained other than 15 (5 or 10 or 20 or 25)
    If 15 was not there on first draw, then there are 8 tickets in box which contain a multiple of 3 out of 24 tickets. (25/3 = 8) – because 15 is already out from the box
    So probability = 8/24 (24 tickets remaining after 1st draw)
    Add the cases for probability of multiple of 3 on second ticket, so prob. = 7/24 + 8/24 = 15/24 (added the cases because we want one of these cases to happen and not both)
    So required probability = 1/5 * 15/24 = 1/8 (multiplied the cases because we want both to happen)
  9. What is the probability of selecting a two digit number at random such that it is a multiple of 2 but not a multiple of 14?
    A) 17/60
    B) 11/27
    C) 13/30
    D) 31/60
    E) 17/30
    View Answer
    Option C
    Solution:
    There are 90 two digit numbers (10-99)
    Multiple of 2 = 90/2 = 45
    Multiple of 14 = 90/14 = 6
    Since all multiples of 14 are also multiple of 2, so favorable events = 45 – 6 = 39
    So required probability = 39/90 = 13/30
  10. There are 2 urns. 1st urn contains 6 white and 6 blue balls. 2nd urn contains 5 white and 7 black balls. One ball is taken at random from first urn and put to second urn without noticing its color. Now a ball is chosen at random from 2nd urn. What is the probability of the second ball being a white colored ball?
    A) 11/13
    B) 6/13
    C) 5/13
    D) 5/12
    E) 11/12
    View Answer
    Option A
    Solution:
    Case 1: first was a white ball
    Now it is put in second urn, so total white balls in second urn = 5+1 = 6, and total balls in second urn = 12+1 = 13
    So probability of white ball from second urn = 6/13
    Case 2: first was a blue ball
    Now it is put in second urn, so total white balls in second urn remain 5, and total balls in second urn = 12+1 = 13
    So probability of white ball from second urn = 5/13
    So required probability = 6/13 + 5/13 = 11/13 (added the cases because we want one of these cases to happen and not both)

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38 Thoughts to “Quantitative Aptitude: Probability Set 1”

  1. ^^^Jaga^^^....
    February 17, 2017 at 11:50 pm

    mam… i think q4 ans is wrong….

    Reply
  2. ^^^Jaga^^^....
    February 18, 2017 at 12:00 am

    q4…………………..4c2+5c2+4c1*5c1/12c2 =6/11

    Reply
    1. Shubhra
      February 18, 2017 at 7:21 am

      Corrected

      Reply
  3. Blak
    May 31, 2017 at 1:26 pm

    Q9. there are 7 mutiples 14,28,42,56,70,84,98

    Reply
  4. Ayushi
    August 1, 2017 at 9:15 pm

    mam plz can you give the whole data or info related to cards ?plz

    Reply
  5. the walking dead
    November 9, 2017 at 1:14 pm

    🙂

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