Quantitative Aptitude: Probability Questions – Set 19

  1. Two dices are rolled down simultaneously, then find the probability of getting sum of results on both dices more than 8.
    2/15
    4/19
    1/8
    5/18
    3/20
    Option D
    possible cases=(3,6), (4,5), (4,6), (5,4), (5,5)
    required probability=10/36=5/18

     

  2. A bag contains 6 blue balls and 8 pink balls. If a ball is drawn randomly from it, then find the probability of getting either pink ball or blue ball.
    4
    5
    1
    1/4
    2/5
    Option C
    required probability=6/14+8/14=14/14=1

     

  3. In a box there are 4 red balls and 3 blue balls. If two balls are drawn at random, then find the probability of that none is blue.
    2/5
    2/7
    5/8
    4/15
    4/18
    Option B
    required probability=(4C2)/(7C2)
    =4*3/7*6=2/7

     

  4. A basket contains 5 white balls , 4 red balls, 2 blue balls and 3 yellow balls. If four balls are picked at randomly. What is the probability that 2 are blue and 2 are red ?
    5/1002
    8/968
    12/1005
    8/950
    6/1001
    Option E
    required=(2C2)*(4C2)
    =(2*1/2*1)*(4*3/2*1)=1*6
    total=14C4=14*13*12*11/4*3*2*1
    =7*13*11
    probability=1*6/7*13*11=6/1001

     

  5. When two dices are thrown simultaneously, then find the probability that sum is a prime number which is less than 8 ?
    12/38
    20/36
    20/35
    13/36
    15/48
    Option D
    prime numbers=2,3,5,7
    possibility of 2=(1,1)
    possibility of 3=(1,2), (2,1)
    possibility of 5=(1,4), (4,1), (3,2), (2,3)
    possibility of 7=(1,6), (6,1), (2,5), (5,2), (3,4), (4,3)
    required=1+2+4+6=13
    total=6^2=36
    probability=13/36

     

  6. When two coins are tossed simultaneously, then find the probability of getting at least one head.
    4/5
    3/4
    8/9
    7/12
    2/15
    Option B
    probability=3/2^2=3/4

     

  7. If from a pack of 52 cards, 1 cards is drawn at randomly, find the probability of the card is an ace.
    2/15
    1/13
    4/15
    2/25
    8/18
    Option B
    required=4C1=4
    total=52C1
    probability=4/52=1/13

     

  8. Two cards are drawn at random from a pack of 52 cards. What is the probability that both are the queen cards ?
    2/221
    4/225
    5/228
    1/221
    8/125
    Option D
    required=4C2=4*3/2*1=12/2=6
    total=52C2=52*51/2
    probability=6/26*51=1/221

     

  9. In how many ways letters of the word ‘LAPTOP’ be arranged such that consonants always come together ?
    50
    75
    40
    72
    80
    Option D
    required ways=3!*4!/2!=72 ways

     

  10. A bag contains 4 red balls and 8 balls. If two balls are taken out from the bag, then find probability of at least one ball being red ?
    40/85
    48/65
    55/64
    35/66
    40/86
    Option D
    favorable cases=(1 blue and 1 red) or ( 2 red)
    probability=(4C1)*(8C1)/(12C2)+(4C2)/(12C2)
    =(4*8/12*11/2*1)+(4*3/2*1/12*11)
    =(4*8/11*6)+(2*3/12*11)=16/33+1/22
    =32+3/66=35/66

     

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