Quants Questions: Probability Set 3

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 !!

1. 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!
   
   Answer

   B) 14! * 2
   Explanation :(16 – 2)! * 2 = 14! * 2
   
   
   
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
   
   Answer

   A)1/3
   Explanation :
   6C₂ = 6*5/2*1 = 30/2 = 15
   10C₂  = 10*9/1*2 = 45
   P =15/45 = 1/3
   
   
   
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
   
   Answer

   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
   
   
   
4. 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
   
   Answer

   D)1/11
   Explanation :
   12C2 = 12*11/2 = 66
   4C2 = 4*3/2 = 12/2 = 6
   P = 6/66 = 1/11
   
   
   
5. 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
   
   Answer

   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
   
   
   
6. 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
   
   Answer

   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
   
   
   
7. 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
   
   Answer

   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
   
   
   
8. In how many different ways the word FAVOUR can be arranged ?
   A)820
   B)530
   C)560
   D)760
   
   Answer

   D)720
   Explanation :6! = 6*5*4*3*2*1 = 720
   
   
   
9. 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
   
   Answer

   B)3/8
   Explanation :
   Total = 5+3 = 8
   Red = 3
   P = 3/8
   
   
   
10. 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
    
    Answer

    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