Quantitative Aptitude: Probability Questions – Set 3

Probability Questions for Bank PO Exams – SBI PO, NIACL, NICL, BoB PO, IBPS PO, and other exams

  1. There are 100 tickets in a box numbered 1 to 100. 3 tickets are drawn at one by one. Find the probability that the sum of number on the tickets is odd.
    A) 2/7
    B) 1/2
    C) 1/3
    D) 2/5
    E) 3/7
    View Answer
    Option B
    Solution:
    There will be 4 cases
    Case 1: even, even, odd
    Prob. = 1/2 × 1/2 × 1/2
    Case 2: even, odd, even
    Prob. = 1/2 × 1/2 × 1/2
    Case 3: odd, even, even
    Prob. = 1/2 × 1/2 × 1/2
    Case 4: odd, odd, odd
    Prob. = 1/2 × 1/2 × 1/2
    Add all the cases, required prob. = 1/2
  2. There are 4 green and 5 red balls in first bag. And 3 green and 5 red balls in second bag. One ball is drawn from each bag. What is the probability that one ball will be green and other red?
    A) 85/216
    B) 34/75
    C) 95/216
    D) 35/72
    E) 13/36
    View Answer
    Option D
    Solution:
    Case 1:first green, second red
    Prob. = 4/9 × 5/8 = 20/72
    Case 2:first red, second green
    Prob. = 5/9 × 3/8 = 15/72
    Add the two cases
  3. A bag contains 2 red, 4 blue, 2 white and 4 black balls. 4 balls are drawn at random, find the probability that at least one ball is black.
    A) 85/99
    B) 81/93
    C) 83/99
    D) 82/93
    E) 84/99
    View Answer
    Option A
    Solution:
    Prob. (At least 1 black) = 1 – Prob. (None black)
    So Prob. (At least 1 black) = 1 – (8C4/12C4) = 1 – 14/99
  4. Four persons are chosen at random from a group of 3 men, 3 women and 4 children. What is the probability that exactly 2 of them will be men?
    A) 1/9
    B) 3/10
    C) 4/15
    D) 1/10
    E) 5/12
    View Answer
    Option B
    Solution:
    2 men means other 2 woman and children
    So prob. = 3C2 × 7C2 /10C4 = 3/10
  5. Tickets numbered 1 to 120 are in a bag. What is the probability that the ticket drawn has a number which is a multiple of 3 or 5?
    A) 8/15
    B) 5/16
    C) 7/15
    D) 3/10
    E) 13/21
    View Answer
    Option C
    Solution:
    Multiples of 3 up to 120 = 120/3 = 40
    Multiples of 5 up to 120 = 120/5 = 24 (take only whole number before the decimal part)
    Multiple of 15 (3×5) up to 120 = 120/15 = 8
    So total such numbers are = 40 + 24 – 8 = 56
    So required probability = 56/120 = 7/15
  6. There are 2 people who are going to take part in race. The probability that the first one will win is 2/7 and that of other winning is 3/5. What is the probability that one of them will win?
    A) 14/35
    B) 21/35
    C) 17/35
    D) 19/35
    E) 16/35
    View Answer
    Option D
    Solution:
    Prob. of 1st winning = 2/7, so not winning = 1 – 2/7 = 5/7
    Prob. of 2nd winning = 3/5, so not winning = 1 – 3/5 = 2/5
    So required prob. = 2/7 * 2/5 + 3/5 * 5/7 = 19/35
  7. Two cards are drawn at random from a pack of 52 cards. What is the probability that both the cards drawn are face card (Jack, Queen and King)?
    A) 11/221
    B) 14/121
    C) 18/221
    D) 15/121
    E) 14/221
    View Answer
    Option A
    Solution:
    There are 52 cards, out of which there are 12 face cards.
    So probability of 2 face cards = 12C2/52C2 = 11/221
  8. A committee of 5 people is to be formed from among 4 girls and 5 boys. What is the probability that the committee will have less number of boys than girls?
    A) 7/12
    B) 7/15
    C) 6/13
    D) 5/14
    E) 7/13
    View Answer
    Option D
    Solution:
    Case 1: 1 boy and 4 girls
    Prob. = 5C1 × 4C4/9C5 = 5/146
    Case 2: 2 boys and 3 girls
    Prob. = 5C2 × 4C3/9C5 = 40/126
    Add the two cases = 45/126 = 5/14
  9. A bucket contains 2 red balls, 4 blue balls, and 6 white balls. Two balls are drawn at random. What is the probability that they are not of same color?
    A) 5/11
    B) 14/33
    C) 2/5
    D) 6/11
    E) 2/3
    View Answer
    Option E
    Solution:
    Three cases
    Case 1: one red, 1 blue
    Prob = 2C1 × 4C1 / 12C2 = 4/33
    Case 2: one red, 1 white
    Prob = 2C1 × 6C1 / 12C2 = 2/11
    Case 3: one white, 1 blue
    Prob = 6C1 × 4C1 / 12C2 = 4/11
    Add all cases
  10. A bag contains 5 blue balls, 4 black balls and 3 red balls. Six balls are drawn at random. What is the probability that there are equal numbers of balls of each color?
    A) 11/77
    B) 21/77
    C) 22/79
    D) 13/57
    E) 15/77
    View Answer
    Option E
    Solution:
    5C2× 4C2× 3C2/ 12C6

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13 Thoughts to “Quantitative Aptitude: Probability Questions – Set 3”

  1. •?((¯°·._.• ąkduuu •._.·°¯))؟•

    probability :||
    i skip

  2. Preeti

    2nd q? mine ans is 35/72

  3. Preeti

    4/9*5/8 + 5/9*3/8 = 35/72

    1. yes yes

      5 ki jagah 4 se calculate kar diya

      1. Vision

        So Prob. (At least 1 black) = 1 – (8C4/12C4) = 14/99
        Admin see that
        So Prob. (At least 1 black) = 1 – (8C4/12C4) = 1-14/99=85/99 hoga

  4. jaga

    thank u mam…:)

  5. Ayushi

    8th ka solution correct h ky

    1. prob. that sum of number on the tickets is odd to be found

  6. Pawan Charan

    8 th question answer is 5/14 please correct it
    by the way thank you very much for the questions they are really good and helpful tooo

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