# Aptitude Questions: Probability Set 10

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 six-digit is to be formed from the given numbers 1, 2, 3, 4, 5 and 6. Find the probability that the number is divisible by 4.
a) 3/17
b) 4/15
c) 4/19
d) 4/17
e) None of these
Explanation :
For a number to be divisible by 4, the last two digit should be divisible by 4.
So possible cases – 12, 16, 24, 32, 36, 52, 56, 64 (last two digits)
So favourable outcomes = 24 +24 +24 +24 + 24+ 24+24+24 = 192
So p = 192/720 = 4/15

2. A bag contains 6 red balls and 7 white balls. Another bag contains 5 red balls and 3 white balls. One ball is selected from each. Find the probability that one ball is red and one is white?
a) 53/104
b) 47/104
c) 63/104
d) 51/104
e) None of these
Explanation :
(6/13)*(3/8) + (7/13)*(5/8) =  53/104

3. A lottery is organised by the college ABC through which they will provide scholarship of rupees one lakhs to only one student. There are 100 fourth year students, 150 third year students, 200 second year students and 250 first year students. What is the probability that a second year student is choosen.
a) 1/7
b) 2/7
c) 3/7
d) 4/7
e) None of these
Explanation :
Second year students = 200
so, P = 200/700 = 2/7

4. A card is drawn from a pack of 52 cards. The card is drawn at random; find the probability that it is neither club nor queen?
a) 4/13
b) 5/13
c) 7/13
d) 9/13
e) None of these
Explanation :
1 – [13/52 + 4/52 – 1/52] = 9/13

5. A box contains 50 balls, numbered from 1 to 50. If three balls are drawn at random with replacement. What is the probability that sum of the numbers are odd?
a) 1/2
b) 1/3
c) 2/7
d) 1/5
e) None of these
Explanation :
There are 25  odd and 25 even numbers  from 1 to 50.
Sum will be odd if = odd + odd + odd, odd + even + even, even + odd + even, even+ even + odd
P= (1/2)*(1/2)*(1/2) + (1/2)*(1/2)*(1/2) + (1/2)*(1/2)*(1/2) + (1/2)*(1/2)*(1/2)
=4/8 = ½

6. From a pack of cards, if three cards are drawn at random one after the other with replacement, find the probability that one is ace, one is jack and one is queen?
a) 16/7725
b) 16/5525
c) 18/5524
d) 64/5515
e) None of these
Explanation :
(4c1 + 4c1 + 4c1)/(52c3)

7. A and B are two persons sitting in a circular arrangement with 8 other persons. Find the probability that both A and B sit together.
a) 1/9
b) 2/7
c) 2/9
d) 2/5
e) None of these
Explanation :
Total outcomes = (10 -1)!  = 9!
Favourable outcomes = (9 -1)!*2!
So p = 2/9

8. Find the probability that in a random arrangement of the letter of words in the word ‘PROBABILITY’ the two I’s come together.
a) 2/11
b) 1/11
c) 3/11
d) 4/11
e) None of these
Explanation :
Total outcomes = 11!/(2!*2!)
favourable outcomes = (10!*2!)/(2!*2!)
p = 2/11

9. In a race of 12 cars, the probability that car A will win is 1/5 and of car B is 1/6 and that of car C is 1/3.  Find the probability that only one of them won the race.
a) 2/7
b) 7/10
c) 9/10
d) 3/7
e) None of these
Explanation :
1/5 + 1/6 + 1/3= 7/10 (all events are mutually exclusive)

10. A bag contains 3 red balls and 8 blacks ball and another bag contains 5 red balls and 7 blacks balls, one ball is drawn at random from either of the bag, find the probability that the ball is red.
a) 93/264
b) 95/264
c) 91/264
d) 97/264
e) None of these