Quants Questions: Probability Set 1

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. A five digit number is formed with the digits 0,1,2,3 and 4 without repetition.Find the chance that the number is divisible by 5
   A)3/5
   B)1/5
   C)2/5
   D)4/5
   
   Answer

   Answer -B) 1/5
   Explanation :
   5 digit number = 5! = 120
   Divisible by 5 then the last digit should be 0
   Then the remaining position have the possibility = 4! =24
   P = (4!/5!) = 24/120 = 1/5
   
   
   
2. A bag contain  6 white balls and 4 red balls .Three balls are drawn randomly.What is the probability that one ball is red and other 2 are white
   A)1/2
   B)2/1
   C)3/2
   D)1/3
   
   Answer

   Answer -A) 1/2
   Explanation :
   Total no of balls = 6+ 4 = 10
   3 balls drawn = 10C₃ =(10×9×8)/(3×2×1) =120
   one ball is red and other 2 are white = 4C₁×6C₂   
     4C₁×6C2 =(4×6×5)/(1×2)= 60
   P = 60/120 = ½
   
   
   
3. A box contain 10 red balls, 7 green balls and 12 blue balls. A ball is drawn at random. What is the probability that the ball drawn is either red or green ?
   A)7/29
   B)12/29
   C)17/29
   D)10/29
   
   Answer

   Answer – C) 17/29
   Explanation :
   Total no of balls =10+7+12 = 29
   P(R) =10/29
   P(G) = 7/29
   P(Either red or green) = 10/29 + 7/29 = 17/29
   
   
   
4. A dice is thrown twice . What is the probability that at least one of them comes up with number 4
   A)12/36
   B)11/36
   C)1/6
   D)11/6
   
   Answer

   Answer -B) 11/36
   Explanation :
   
   
5. From a group of 5 men and 2 women , 2 persons are selected at random. Find the probability that at least one woman is selected ?
   A)11/7
   B)21/11
   C)11/21
   D)1/21
   
   Answer

   Answer -C)11/21
   Explanation :
   n(S) = 7C₂  = (7×6)/(1×2) = 21
   n(E) = 2C2+5C_{1 *} 2C_{1 = 1+11}
   P = n(E)/n(S) = 11/21
   
   
   
6. A bag contains 11 red and 5 green balls. Find the probability that 4 balls  are red and 3 balls are green when 7 balls  are drawn at random.
   A)16/52
   B)15/52
   C)11/52
   D)10/52
   
   Answer

   Answer -B) 15/52
   Explanation :
   n(S) = 16C₇ = 11440
   n(E) = 11C₄ ×5C₃ = 330×10 = 3300
   P = n(E)/ n(S) = 3300/11440 = 15/52
   
   
   
7. Four different objects 1,2,3 are distributed at random in four places. What is the probability  that none of the objects occupies the place corresponding to its number ?
   A)1/6
   B)1/3
   C)1/2
   D)1
   
   Answer

   Answer – C) ½
   Explanation :
   PLACE:   1   2   3   4
   Random :  2134 , 2143 , 2314 ,2341 , 2413 ,2431
   None of the objects occupies the place of that number = 2143 ,2341,2413
   n(S) = 6, n(E) = 3
   p = 3/6 = ½
   
   
   
8. A box contain 8 red balls, 6 green balls and 8 blue balls. A ball is drawn at random. What is the probability that the ball drawn is neither red nor green ?
   A)10/29
   B)2/11
   C)11/4
   D)4/11
   
   Answer

   Answer -D) 4/11
   Explanation :
   Total no of balls =8+6+8 = 22
   P(B) =8/22
   P(neither red nor green) = 8/22 = 4/11
   
   
   
9. A box contains 5 green , 4 yellow and 3 white marbles. Three marbles are drawn at random. What is the probability that they are not of the same colour ?
   A)40/44
   B)44/41
   C)41/44
   D)40/39
   
   Answer

   Answer -C) 41/44
   Explanation :
   n(E) = 5C₃₊ 4C₃₊3C_{3 = 10+4+1 = 15
   n(S) =} 12C_{3 = 220}
   P = n(E)/ n(S) = 15/220 =3/44
   Required probability = 1-3/44 = 41/44
   
   
   
10. Two dice are thrown simultaneously .What is the probability of getting 2 numbers whose product is even ?
    A)3/4
    B)4/3
    C)1/4
    D)1/3
    
    Answer

    Answer -A) 3/4
    Explanation :