Hello Aspirants. Welcome to Online** Quantitative Aptitude Section** 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 bank exams !!

Questions Penned by Yogit

**A bag contains 5 red and 7 white balls. Four balls are drawn out one by one and not replaced. What is the probability that they are alternatively of different colours?**

a) 7/99

b) 11/99

c) 14/99

d) 19/99

e) None of theseAnswer –**c) 14/99**

**Explanation :**

Balls are picked in two manners – RWRW or WRWR

So probability = (5/12)*(7/11)*(4/10)*(6/9) + (7/12)*(5/11)*(6/10)*(4/9) = 14/99**P and Q are sitting in a ring with 11 other persons. If the arrangement of 11 persons is at random, then the probability that there are exactly 4 persons between them?**

a) 1/3

b) 1/4

c) 1/5

d) 1/6

e) None of theseAnswer –**d) 1/6**

**Explanation :**

Fix the position of P, then Q can be sit in 12 positions, so total possible outcome = 12

Now, exactly 4 persons are sitting between them. This can be done in two ways as shown in figure, so favourable outcomes = 2

So, probability = 2/12 = 1/6**10 persons are seated around a round table. What is the probability that 4 particular persons are always seated together?**

a) 1/21

b) 4/21

c) 8/21

d) 11/21

e) None of theseAnswer –**a) 1/21**

**Explanation :**

Total outcomes = (10 -1)! = 9!

Favourable outcomes = 6!*4! (4 person seated together and 6 other persons seated randomly, so they will sit in (7-1)! Ways and those 4 persons can be arranged in 4! ways)

So probability = 1/21**A box contains 4 red, 5 black and 6 green balls. 3 balls are drawn at random. What is the probability that all the balls are of same colour?**

a) 33/455

b) 34/455

c) 44/455

d) 47/455

e) None of theseAnswer –**b) 34/455**

**Explanation :**

(4c3 + 5c3 + 6c3)/15c3 = 34/455**An apartment has 8 floors. An elevator starts with 4 passengers and stops at 8 floors of the apartment. What is the probability that all passengers travels to different floors?**

a) 109/256

b) 135/256

c) 105/256

d) 95/256

e) None of theseAnswer –**c) 105/256**

**Explanation :**

Total outcomes = 8*8*8*8

Favourable outcomes = 8*7*6*5 (first person having 8 choices, after that second person have 7 choices and so on)

So, probability = 105/256**A speak truth in 60% cases and B in 80% cases. In what percent of cases they likely to contradict each other narrating the same incident?**

a) 9/25

b) 7/25

c) 11/25

d) 13/25

e) None of theseAnswer –**c) 11/25**

**Explanation :**

P(A) = 3/5 and P(B) = 4/5. Now they are contradicting means one is telling truth and other telling the lie. So,

Probability = (3/5)*(1/5) + (2/5)*(4/5)**A box contains 30 electric bulbs, out of which 8 are defective. Four bulbs are chosen at random from this box. Find the probability that at least one of them is defective?**

a) 432/783

b) 574/783

c) 209/784

d) 334/784

e) None of theseAnswer –**b) 574/783**

**Explanation :**

1 – 22c4/30c4 = 1 – 209/783 = 574/783**Two person A and B appear in an interview. The probability of A’s selection is 1/5 and the probability of B’s selection is 2/7. What is the probability that only one of them is selected?**

a) 11/35

b) 12/35

c) 13/35

d) 17/35

e) None of theseAnswer –**c) 13/35**

**Explanation :**

A selects and B rejects + B selects and A rejects = (1/5)*(5/7) + (4/5)*(2/7) = 13/35**A 4- digit number is formed by the digits 0, 1, 2, 5 and 8 without repetition. Find the probability that the number is divisible by 5.**

a) 1/5

b) 2/5

c) 3/5

d) 4/5

e) None of theseAnswer –**b) 2/5**

**Explanation :**

Total possibility = 5*4*3*2

Favourable outcomes = 2*4*3*2 (to be divisible by 5 unit digit can be filled with only 0 or 5, so only two possibilities are there, then the remaining can be filled in 4, 3 and 2 ways respectively)

so probability = 2/5**A bag contains 6 red balls and 8 green balls. 2 balls are drawn at random one by one with replacement. Find the probability that both the balls are green**

a) 16/49

b) 25/49

c) 12/49

d) 21/49

e) None of theseAnswer –**a) 16/49**

**Explanation :**

(8c1)/(14c1) * (8c1)*(14c1) = 16/49

**Note:** Dear Readers if you have any doubt in any chapter in Quants you can ask here. We will clear your doubts

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