Quantitative Aptitude: Probability Questions – Set 13

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