Quantitative Aptitude: Probability Questions – Set 13

Mani
  1. A bag contains 5 ruby balls and 7 black balls. Two balls are drawn at random without replacement, and then find the probability of that one is ruby and other is black?
    35/66
    41/69
    36/68
    30/60
    None of these
    Option A
    (First ruby ball is drawn and then black ball is drawn) + (first black ball is drawn and then ruby ball is drawn)
    (5/12)*(7/11)+(7/12)*(5/11) = 35/66

     

  2. A bag contains 3 ruby balls and 8 blue ball and another bag contains 5 ruby balls and 7 blue balls, one ball is drawn at random from either of the bag, find the probability that the ball is ruby?
    85/265
    91/264
    70/250
    75/310
    None of these
    Option B
    Probability=Probability of selecting the bag and probability of selecting ruby ball
    (1/2)*(3/11) + (1/2)*(5/12) =91/264

     

  3. X and Y are two persons standing in a circular arrangement with 10 more people. Find the probability that exactly 3 persons are seated between X and Y?
    1/5
    3/9
    2/11
    1/10
    None of these
    Option C
    Fix X at one point then number of places where Y can be seated is 11.
    Now, exactly three persons can be seated between X and Y, soonly two places where Y can be seated.
    So, X = 2/11

     

  4. 12 friends are seated at a circular table. Find the probability that 3 particular friends always seated together?
    4/52
    5/50
    2/15
    3/55
    None of these
    Option D
    Total probability=(12-1)! = 11!
    Desired Probability = (10 – 1)! = 9!
    So, Probability= (9! *3!) /11! =3/55

     

  5. Find the probability that in a leap year, the numbers of Wednesday are 53?
    2/7
    1/7
    3/7
    4/7
    5/7
    Option A
    In a leap year there are 52 complete weeks i.e. 364 days and 2 more days.
    These 2 days can be SM, MT, TW, WT, TF, FS, and SS.
    So Probablity of Wednesday = 2/7

     

  6. Study the following and answer the questions:
    A carton contains 6 ruby balls and 8 grey balls. Two balls are drawn at random one after one with replacement. What is the probability that both the balls are grey?
    16/49
    15/45
    10/50
    14/48
    None of these
    Option A
    Probability = (8/14)*(8/14) = 64/196 =16/49

     

  7. If the first one is grey and second one is ruby,find the following?
    15/49
    13/49
    10/49
    11/49
    12/49
    Option E
    Probability = (8/14)*(6/14) =48/196=12/49

     

  8. If the both the balls are ruby,find the following?
    10/49
    9/49
    11/49
    13/49
    None of these
    Option B
    Probability = (6/14)*(6/14)=36/196=9/49

     

  9. A carton contains 6 beige, 5 grey and 4 ruby balls. Two balls are drawn at random. What is the probability that there is no ruby ball?
    10/21
    2/50
    3/15
    11/21
    None of these
    Option D
    Total balls in carton = 15
    Not ruby ball means grey or beige ball i.e. any of (5+6) = 11 balls
    So probability = 11C2 / 15C2 =11/21

     

  10. There are 4 ruby balls, 5 white and 3 grey balls. 3 balls are chosen at random. What is the probability that there is at most 1 grey ball?
    48/55
    40/55
    42/54
    50/82
    None of these
    Option A

     


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