# Aptitude Questions: Probability Set 11

Hello Aspirants. Welcome to Online Quantitative Aptitude Section in AffairsCloud.com. Here we are creating question sample in Probability, which is common for all the  competitive exams. We have included Some questions that are repeatedly asked in bank exams !!

Questions Penned by Yogit

1. A bag contains 5 red and 7 white balls. Four balls are drawn out one by one and not replaced. What is the probability that they are alternatively of different colours?
a) 7/99
b) 11/99
c) 14/99
d) 19/99
e) None of these
Explanation :
Balls are picked in two manners – RWRW or WRWR
So probability = (5/12)*(7/11)*(4/10)*(6/9) + (7/12)*(5/11)*(6/10)*(4/9) = 14/99
2. P and Q are sitting in a ring with 11 other persons. If the arrangement of 11 persons is at random, then the probability that there are exactly 4 persons between them?
a) 1/3
b) 1/4
c) 1/5
d) 1/6
e) None of these
Explanation :
Fix the position of P, then Q can be sit in 12 positions, so total possible outcome = 12
Now, exactly 4 persons are sitting between them. This can be done in two ways as shown in figure, so favourable outcomes = 2
So, probability = 2/12 = 1/6
3. 10 persons are seated around a round table. What is the probability that 4 particular persons are always seated together?
a) 1/21
b) 4/21
c) 8/21
d) 11/21
e) None of these
Explanation :
Total outcomes = (10 -1)! = 9!
Favourable outcomes = 6!*4! (4 person seated together and 6 other persons seated randomly, so they will sit in (7-1)! Ways and those 4 persons can be arranged in 4! ways)
So probability = 1/21
4. A box contains 4 red, 5 black and 6 green balls. 3 balls are drawn at random. What is the probability that all the balls are of same colour?
a) 33/455
b) 34/455
c) 44/455
d) 47/455
e) None of these
Explanation :
(4c3 + 5c3 + 6c3)/15c3 = 34/455
5. An apartment has 8 floors. An elevator starts with 4 passengers and stops at 8 floors of the apartment. What is the probability that all passengers travels to different floors?
a) 109/256
b) 135/256
c) 105/256
d) 95/256
e) None of these
Explanation :
Total outcomes = 8*8*8*8
Favourable outcomes = 8*7*6*5 (first person having 8 choices, after that second person have 7 choices and so on)
So, probability = 105/256
6. A speak truth in 60% cases and B in 80% cases. In what percent of cases they likely to contradict each other narrating the same incident?
a) 9/25
b) 7/25
c) 11/25
d) 13/25
e) None of these
Explanation :
P(A) = 3/5 and P(B) = 4/5. Now they are contradicting means one is telling truth and other telling the lie. So,
Probability = (3/5)*(1/5) + (2/5)*(4/5)
7. A box contains 30 electric bulbs, out of which 8 are defective. Four bulbs are chosen at random from this box. Find the probability that at least one of them is defective?
a) 432/783
b) 574/783
c) 209/784
d) 334/784
e) None of these
Explanation :
1 – 22c4/30c4 = 1 – 209/783 = 574/783
8. Two person A and B appear in an interview.  The probability of A’s selection is 1/5 and the probability of B’s selection is 2/7. What is the probability that only one of them is selected?
a) 11/35
b) 12/35
c) 13/35
d) 17/35
e) None of these
Explanation :
A selects and B rejects + B selects and A rejects = (1/5)*(5/7) + (4/5)*(2/7) = 13/35
9. A 4- digit number is formed by the digits 0, 1, 2, 5 and 8 without repetition. Find the probability that the number is divisible by 5.
a) 1/5
b) 2/5
c) 3/5
d) 4/5
e) None of these
Explanation :
Total possibility = 5*4*3*2
Favourable outcomes = 2*4*3*2  (to be divisible by 5 unit digit can be filled with only 0 or 5, so only two possibilities are there,  then the remaining can be filled in 4, 3 and 2 ways respectively)
so probability = 2/5
10. A bag contains 6 red balls and 8 green balls. 2 balls are drawn at random one by one with replacement. Find the probability that both the balls are green
a) 16/49
b) 25/49
c) 12/49
d) 21/49
e) None of these