Quants Questions : Probability Set 4

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. Q(1-3): An urn contain 6 orange, 4 green,3 pink and 4 black balls
   If 3 balls are picked at random, what is the probability that all are pink ?
   A)2/650
   B)1/680
   C)4/630
   D)3/680
   
   Answer

   B)1/680
   Explanation :
   17C3 = 17*16*15/3*2*1 = 4080/6 = 680
   3C3 = 1
   P = 1/680
   
   
   
2. If 5 balls are picked at random, what is the probability that none are orange ?
   A)33/442
   B)442/33
   C)15/167
   D)23/235
   
   Answer

   A)33/442
   Explanation :
   17C5 = 17*16*15*14*13/5*4*3*2*1 = 742560/120 = 6188
   11C5 = 11*10*9*8*7/5*4*3*2*1 = 55440/120 = 462
   P = 462/6188 = 33/442
   
   
   
3. If 3 balls are drawn at random, what is the probability that 1 is green and the other 2 are black ?
   A)2/85
   B)4/87
   C)1/85
   D)3/85
   
   Answer

   D)3/85
   Explanation :
   17C3 = 17*16*15/3*2*1 = 4080/6 = 680
   4C1 × 4C2 = 4*4*3/2*1 = 24
   P = 24/680 = 3/85
   
   
   
4. There are 8 positive numbers and 6 negative numbers. 4 numbers are chosen at random and multiplied. Find the probability that the product is a positive number ?
   A)1001/505
   B)101/505
   C)505/1001
   D)450/965
   
   Answer

   C)505/1001
   Explanation :
   14C4  = 14*13*12*11/4*3*2*1 = 1001
   4 No positive+4 no negative + (2 no positive * 2 no negative)
   = 6C4 + 8C4 +(6C2 ×8C2) = 15+70+15*28 = 505
   P = 505/1001
   
   
   
5. A five digit number is formed with the digit 1,2,3,4 and 5 without repetition. Find the chance that the number is divisible by 5 ?
   A)1/4
   B)1/5
   C)1/3
   D)1/2
   
   Answer

   B)1/5
   Explanation :
   5! = 5*4*3*2*1 = 120
   4! = 4*3*2*1 = 24
   P = 24/120 = 1/5
   
   
   
6. A bag contains 6 red, 5 blue and 2 green balls. If 2 balls are picked at random, what is the probability that both are green?
   A)1/78
   B)2/75
   C)4/89
   D)None
   
   Answer

   A)1/78
   Explanation :
   13C2 = 13*12/2 =78
   2C2 = 1
   P = 1/78
   
   
   
7. If You toss a coin and roll a die. What is the probability of getting a head and a 3 on the die?
   A)1/10
   B)1/8
   C)1/12
   D)2/3
   
   Answer

   C)1/12
   Explanation :1/2 * 1/6 = 1/12
   
   
   
8. From a pack of 52 cards, 3 cards are drawn. What is the probability that one is ace, one is queen and one is jack?
   A) 12/5520
   B) 15/4525
   C) 13/5005
   D) 16/5525
   
   Answer

   D) 16/5525
   Explanation :
   =4C1×4C1×4C1 / 52C3
   =4×4×4 / 22100
   =16/5525
   
   
   
9. Two dice are thrown simultaneously. Find the probability of getting a multiple of 2 on one dice and multiple of 3 on the other dice.
   A)10/28
   B)11/38
   C)11/36
   D)12/35
   
   Answer

   C)11/36
   Explanation :
   n(S) = 36
   n(E) = (2,3),(2,6),(4,3),(4,6),(6,3),(6,6),(3,2),(6,2),(3,4),(6,4),(3,6)
   P = 11/36
   
   
   
10. Two dice are tossed. The probability that the total score is a prime number is
    A)5/12
    B)7/12
    C)6/11
    D)5/7
    
    Answer

    A)5/12
    Explanation :
    E =  (1, 1), (1, 2), (1, 4), (1, 6), (2, 1), (2, 3), (2, 5), (3, 2), (3, 4), (4, 1), (4, 3),
    (5, 2), (5, 6), (6, 1), (6, 5)
    n(E) = 15
    n(S) = 6*6 = 36
    P = 15/36 = 5/12