Quantitative Aptitude: Probability Questions – Set 20

  1. A bag contains 8 green balls and 12 blue balls. If a ball is drawn randomly, then find the probability of getting either green ball or blue ball.
    2
    3
    2/5
    2/3
    1
    Option E
    required = (8C1) + (12C1) = 20
    total = (20C1) = 20
    probability = 20/20 = 1

     

  2. If two cards are drawn randomly from a pack of 52 cards. Then what is the probability of both cards are red cards ?
    28/91
    23/108
    25/102
    8
    17
    Option C
    required = (26C2) = 13 * 25
    Total = (52C2) = 26 * 51
    probability = (13 * 25)/(26 * 51) = 25/102

     

  3. How ,any 4-digit numbers can be formed from the digits 6, 2, 5, 7, 3, which are divisible by 5 and none of the digits is repeated ?
    140
    220
    28
    24
    96
    Option D
    A number to be divisible by 5, unit digit must be 0 or 5.
    So, in 4-digit numbers unit place is required to be filled by digit 5 and rest three places of required 4-digit numbers will be filled by rest 4 digit.
    numbers of ways = 4! = 4 * 3 * 2 * 1 = 24

     

  4. Out of 52 playing cards two cards is picked randomly, then what is the probability of getting that one red king and one black queen ?
    2/663
    5/13
    8/58
    5
    14
    Option A
    required = (2C1) * (2C1) = 4
    Total = (52C2) = 26 * 51
    probability = 4/(26*51) = 2/663

     

  5. A bag contains 2 red pens, 6 blue pens and 4 green pens. Find the probability of getting two same color pens from the bag ?
    5/8
    2/4
    1/3
    5/6
    4
    Option C
    required = (2C2) + (6C2) + (4C2)
    = 1 + 15 + 6 = 22
    total = (12C2) = 66
    probability = 22/66 = 1/3

     

  6. A basket contains 3 green, 4 orange and 5 pink balls. If two balls are drawn randomly from the basket, then what the probability of selecting that both balls are of different colors ?
    4/65
    57/68
    8/45
    47/66
    4/15
    Option D
    possibility of both balls are different colors = ( 1 green and 1 orange) , (1 orange and 1 pink ), (1 green and 1 pink)
    required = (3C1) * (4C1) + (4C1) * (5C1) + (3C1) * (5C1)
    = 12 + 20 + 15 = 47
    total = (12C2) = 66
    probability = 47/66

     

  7. Sunil threw two dices together. What is the probability of getting that the sum of the two outcomes is 4 ?
    1/8
    1/12
    4
    5
    2
    Option B
    Possibility to get = (2, 2), (3, 1), (1, 3)
    required = 3
    total = 36
    probability = 3/36 = 1/12

     

  8. When three coins are tossed simultaneously, then find the probability of getting at least one tale.
    7/8
    5/8
    1/4
    4/15
    2
    Option A
    possibility = 1 tale or 2 tale or 3 tale
    required = (3C1) + (3C2) + (3C3)
    = 3 + 3 + 1 = 7
    total = 2^3 = 8
    probability = 7/8

     

  9. Four boys and 2 girl sit in a row for presenting their project paper, then what is the probability that they will sit in alternate position ?
    1/6
    2/3
    1/8
    1/15
    2/5
    Option D
    probability = 4! * 2!/6! = 1/15

     

  10. Probability of a question solved by A and B is 1/5 and 1/4 respectively, then find the probability that at least one of them will solve the questions ?
    5/6
    1/4
    11/25
    2/5
    5/9
    Option D
    possibility = 1 – probability of question not solved by anyone
    probability = 1 – (1 – 1/5) * (1 – 1/4)
    = 1-(4/5) * (3/4)
    = 2/5

     

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