Hello Aspirants. Welcome to Online Maths 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 exams !!

**16 persons are participated in a party. In how many different ways can they host the seat in a circular table, if the 2 particular persons are to be seated on either side of the host ?**

A)16! * 2

B) 14! * 2

C) 18! * 2

D)14!

**B) 14! * 2**

Explanation :(16 – 2)! * 2 = 14! * 2

**Out of a total 10 bulbs, 6 bulbs are working inorder. One has to choose 2 bulbs out of 6. What is the probability that all the 2 bulbs will be glowing ?**

A)1/3

B)1/2

C)1/5

D)1/6

**A)1/3**

Explanation :

6C_{2 }= 6*5/2*1 = 30/2 = 15

10C_{2 }= 10*9/1*2 = 45

P =15/45 = 1/3

**In how many different ways can the letters of the word KINETIC arranged so that the vowels never come together ?**

A)5460

B)4600

C)2160

D)5040

**C)2160**

Explanation :

7 letters = 7! /2!= 5040/2 = 2520

Vowels => I I E = 3!/2! =6/2 = 3

Consonants 4 + all vowels considered as 1 = 4+1 = 5 => 5! = 120

120*3 = 360

No of ways the vowels never come together = 2520 – 360 = 2160

**A bag contains 4 black shirts , 3 yellow shirts and 5 red shirts, if 2 shirts are drawn randomly, What is the probability both of them are black?**

A)12/5

B)11

C)1/12

D)1/11

**D)1/11**

Explanation :

12C2 = 12*11/2 = 66

4C2 = 4*3/2 = 12/2 = 6

P = 6/66 = 1/11

**A box contains 10 white balls and 6 black balls. 2 balls are drawn at random. What is the probability that they are of the same colour ?**

A)1/2

B)2

C)1/3

D)1/5

**A)1/2**

Explanation :

10C2 = 10*9/2 = 45

6C2 = 6*5/2 = 15

16C2 = 16*15/2 = 120

P = 45+15/120 = 60/120 = 1/2

**An urn contains 4 brown marbles, 5 green marbles, 2 red marbles and 3 white marbles. If 3 marbles are drawn, what is the probability all of them is green ?**

A)5/182

B)4/187

C)12/187

D)10/183

**A)5/182**

Explanation :

Total = 14

3 marbles drawn = 14C3 = 14*13*12/ 3*2*1 = 364

5C3 = 5*4*3/3*2*1 = 10

P = 10/364 = 5/182

**A basket contains 3 brown and 4 green balls. If three balls are drawn at random ,What is the probability that all the three are same colour?**

A)7/5

B)3/7

C)1/7

D)4/7

**C)1/7**

Explanation :

Total = 3+4 = 7

7C3 = 7*6*5/3*2*1 = 35

3C3 + 4C3 = 1 + 4*3*2 /3*2*1 = 1+4 = 5

P = 5/35 = 1/7

**In how many different ways the word FAVOUR can be arranged ?**

A)820

B)530

C)560

D)760

**D)720**

Explanation :6! = 6*5*4*3*2*1 = 720

**A bag contains 5 white and 3 red balls. One ball is drawn at random. What is the probability that the ball drawn is red?**

A)5/8

B)3/8

C)1/4

D)1/2

**B)3/8**

Explanation :

Total = 5+3 = 8

Red = 3

P = 3/8

**From a group of 4 men ,3 women, 2 persons are selected at random, Find the probability at least one man is selected ?**

A)6/7

B)7/6

C)5/6

D)11/21

**A)6/7**

Explanation :

7C2 = 7*6/2 = 21

4C1*3C1 + 4C2 = 4*3 + (4*3)/2 = 12+6 = 18

P = 18/21 = 6/7

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