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 !!

**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

**B)1/680**

Explanation :

17C3 = 17*16*15/3*2*1 = 4080/6 = 680

3C3 = 1

P = 1/680

**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

**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

**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

**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

**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

**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

**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

**B)1/5**

Explanation :

5! = 5*4*3*2*1 = 120

4! = 4*3*2*1 = 24

P = 24/120 = 1/5

**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

**A)1/78**

Explanation :

13C2 = 13*12/2 =78

2C2 = 1

P = 1/78

**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

**C)1/12**

Explanation :1/2 * 1/6 = 1/12

**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

**D) 16/5525**

Explanation :

=4C1×4C1×4C1 / 52C3

=4×4×4 / 22100

=16/5525

**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

**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

**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

**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

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