# 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