Quantitative Aptitude: Probability Questions – Set 22

  1. Two dice are rolled randomly. Find the probability to get sum is 10.
    2/5
    14
    2/9
    1/12
    5/8
    Option D
    Required = (6 , 4 ) , (4 , 6) , ( 5, 5) = 3
    total = 6 * 6 = 36
    probability = 3/36 = 1/12

     

  2. Two dices are rolled out together, then what is the probability of getting a number of one dice greater than the number of other dice ?
    2/3
    1/6
    3/8
    1/8
    5/6
    Option E
    Non-favorable events = (1 , 1) , (2 , 2) , (3 , 3) , (4 , 4) , (5 , 5) , (6,6) = 6
    total = 6 * 6 = 36
    probability of non-favorable events = 6/36 = 1/6
    probability of favorable events = 1 – 1/6 = 5/6

     

  3. If 2 cards is drawn at randomly from 52 cards, then find the probability of getting both are red cards.
    13/28
    26/105
    28/108
    25/102
    none of these
    Option D
    Required = 26C2 = 26 * 25/2 = 13 * 25
    total = 52C2 = 52 * 51 / 2 = 26 * 51
    probability = 13 * 25 / 26 * 51 = 25 /102

     

  4. In how many ways, we can arrange the letters of the word ‘LIGHT’ ?
    84
    28
    140
    160
    120
    Option E
    Ways = 5! = 5 * 4 * 3 * 2 * 1 = 120

     

  5. In how many different ways, we can arrange the letters of the word ‘MOUSE’ , so that the middle position is always occupied by ‘S’ ?
    25
    24
    48
    42
    68
    Option B
    Ways = 4! = 4 * 3 * 2 * 1 = 24

     

  6. How many ways 6 books can be selected from 14 different books , if two particular books are always selected ?
    495
    480
    231
    384
    520
    Option A
    Available objects = 14 – 2 = 12
    Ways = 12C4 = 12 * 11 * 10 * 9/4 * 3 * 2 * 1 = 495

     

  7. A bag contains 2 white balls, 3 pink balls and 2 black balls. 2 balls are drawn randomly. What is the probability that there is no black balls ?
    8/21
    10/21
    1/8
    3/5
    6/11
    Option B
    Required = 5C2 = 5*4/2 = 10
    total = 7C2 = 7 * 6 / 2 = 21
    probability = 10/21

     

  8. When two coins are tossed simultaneously, then find the probability of getting at least one tail.
    5
    3
    3/4
    1/4
    2/5
    Option C
    Required = ( 1 head , 1 tail ) , ( 2 tails) = (2C1) + (2C2) = 2 + 1 = 3
    total = 2^2 = 4
    probability = 3/4

     

  9. A bag contains 4 red balls, 2 blue balls and 2 green balls . If two balls are drawn randomly from the bag , then find the probability of getting both balls of different color.
    2/7
    5/8
    5/7
    4
    8
    Option C
    probability = 4C1 * 2C1 / 8C2 + 4C1 * 2C1 / 8C2 + 2C1 * 2C1 / 8C2
    (4 * 2 * 2)/ 8 * 7 + (4 * 2 * 2)/ 8 * 7 + (2 * 2 * 2) / 8 * 7 = 2/7 + 2/7 + 1/7 = 5/7

     

  10. A group of students sitting around a rectangular table, find probability of 2 specified students sitting together.
    3/8
    2/7
    8/7
    3/8
    6/11
    Option B
    Favorable cases = 6! * 2!
    total cases = 7!
    probability = 6! * 2! /7! = 2/7

     

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