Probability Quiz for SBI PO / IBPS PO 2017

Directions (1-2): Read the following information to answer the questions. 

There are 9 red, 7 white and 4 black balls in an urn.

Q1. Two balls are drawn at random from the urn. What will be the probability that both the balls are red?  

(a) 18/95

(b) 9/95

(c) 9/10

(d) 8/95

(e) 5/19

Q2. If two balls are selected at random, what is the probability that one ball is white and the other ball is red? 

(a) 91/190

(b) 63/190

(c) 5/19

(d) 4/95

(e) 71/190 

Q3. From a well - Shuffled pack of 52 playing cards, one card is drawn at random. What is the probability, that the card drawn will be a black king?  

(a) 1/26

(b) 7/13

(c) 3/13

(d) 9/13

(e) 1/13

Q4. A die is thrown twice. What is the probability of getting a sum 7 from both the throws? 

(a) 5/18

(b) 1/18

(c) 1/9

(d) 1/6 

(e) 5/36

Q5. A bag contains 7 blue balls and 5 yellow balls. If two balls are selected at random, what is the probability that none is yellow?  

(a) 5/33

(b) 5/22

(c) 7/22

(d) 7/33

(e) 7/66

Directions (6-10): Study the given information carefully to answer the questions that follow. 

An urn contains 4 green, 5 blue, 2 red and 3 yellow marbles. 

Q6. If two marbles are drawn at random, what is the probability that both are red or atleast one is red?  

(a) 26/93

(b) 2/7

(c) 199/366

(d) 135/193

(e) None of these 

Q7. If three marbles are drawn at random, what is the probability that atleast one is yellow?  

(a) 1/5

(b) 199/364

(c) 165/364

(d) 5/9

(e) None of these

Q8. If eight marbles are drawn at random, what is the probability that there are equal number of marbles of each colour?   

(a)  3/8

(b) 351/738

(c) 60/1001

(d) 1/1011

(e) None of these 

Q9. If three marbles are drawn at random, what is the probability that none is green?  

(a) 3/8

(b) 273/748

(c) 30/91

(d) 41/91

(e) None of these 

Q10. If four marbles are drawn at random, what is the probability that two are blue and two are red? 

(a) 10/1001

(b) 7/17

(c) 15/384

(d) 3/5

(e) None of these 

Directions (11-12): Study the given information carefully to answer the questions that follow. 

A basket contains 6 blue, 2 red, 4 green and 3 yellow balls. 

Q11. If 4 balls are picked at random, what is the probability that 2 are red and 2 are green?  

(a) 4/15

(b) 5/27

(c) 1/3

(d) 2/455

(e) None of these 

Q12. If 3 balls are picked at random, what is the probability that none is yellow?  

(a) 3/455 

(b) 1/5

(c) 44/91

(d) 4/5

(e) None of these 

Q13. A bag contains 2 red, 3 green and 2 blue balls. 2 balls to be drawn randomly, what is the probability that the balls drawn contain no blue ball?  

(a) 5/7

(b) 10/21  

(c) 2/7

(d) 11/21

(e) None of these 

Q14. An urn contains 5 red, 4 white and 3 black balls. If two balls are drawn at random, find the probability that both the balls are red.  

(a) 17/45

(b) 5/33

(c) 1/12

(d) 91/190

(e) None of these 

Q15. A box contains 4 black balls, 3 red balls and 5 green balls. 2 balls are drawn from the box at random. What is the probability that both the balls are of the same colour? 

(a) 47/68

(b) 1/6

(c) 19/66

(d) 2/11

(e) None of these 

ANSWERS :

Important Note:

To receive the fastest updates on Bank Exams like IBPS, SBI, RBI, IPPB, etc. as well as all other ongoing as well as forthcoming exams, kindly subscribe to our website. All you have to do is enter your email in the pop-up that appears on the website when you first enter it on the home page. Once you’re subscribed, you will receive all the latest updates concerning all competitive exams.

Read More

Probability Quiz for IPPB / IBPS SO 2017

Q1. What is the rank of the word JAIPUR if all the words formed by the letters of JAIPUR are arranged in ascending order?   
(a) 241
(b) 242
(c) 122
(d) 123
(e) None of these

Q2. In how many ways 3 numbers can be selected from the set of numbers 1, 2, 3….20 such that the selected numbers are in ascending order.  


Q3. How many squares (off all possible dimensions) are there on a chessboard?  
(a) 65
(b) 64
(c) 204
(d) 1296
(e) None of these

Q4. In how many ways 3 playing cards can be selected from a deck of 52 cards such that there is at least one face card.   


Q5. Two teams of 11 students each are formed from 20 students such that exactly three students are common between the two teams. In how many ways can the two teams be formed?  


Q6. If all the words which can be formed by using the letters of the word INDIA are arranged in alphabetical order, find the rank of the word INDIA.  


Q7. A bag contains 3 red balls, 4 green balls and 3 yellow balls. Three balls are randomly selected, find the probability that all the three balls are not of the same colour.  


Q8. Three numbers are randomly selected from the set of natural numbers {1, 2, 3, …..50}, find the probability that these numbers are in AP.


Q9. In a bolt factory machines A, B and C manufacture respectively 25%, 35% and 40% of the total product. Of their output 5, 4, 2 percent are defective bolts. A bolt is drawn at random from the product and is found to be defective. What are the probabilities that it was manufactured by machine A.   

            
Q10. If the letters of the word ‘REGULATION’ be arranged at random, the probability that there will be exactly 4 letters between R and E

ANSWERS :

S1. Ans.(b)

Sol. List of the words comes before JAIPUR in dictionary is 

A- - - - - total words = 5! = 120 

I- - - - - total words = 5! = 120 

JAIPRU 1 word 

JAIPUR

Hence the rank of the word JAIPUR is 120 + 120 + 1 + 1 = 242. 

S2. Ans.(b)

Sol. Let us first solve the question in how many ways 3 numbers can be selected and written in a line. 

- - - 

The answers is 20 × 19 × 18 as first place can be filled in 20 ways, 2nd place can be filled in 19 ways and the 3rd place can be filled in 18 ways. Since we want numbers to be in ascending order, hence out of every 6 permutations only I can be taken. Required number of ways 

S3. Ans.(c)

Sol. There are 64 squares of dimension 1 × 1, there are 49 squares of dimensions 2 × 2, counting in the same way, we get total number of squares in a chess board as:

64 + 49 + 36 + 25 + ….. 4 + 1 = 204

S4. Ans.(b)

Sol. There are 12 face cards, hence the required number of ways

S6. Ans.(c)

Sol. All the words which appear before INDIA are: 

A(- - - -) = 4!/2! = 12 

D(- - - -) = 4!/2! = 12 

IA(- - -) = 3!=6

ID(- - -) = 3! = 6 

II(- - - - ) = 3! = 6  

INA(- -) = 2! = 2

INDAI        = 1 

INDIA

Rank = 46th.  

S8. Ans.(a)

Sol. Suppose the three selected numbers are a, b and c. If these numbers are in AP, then 

2b = a + c, thus a + c must be an even number. This is possible only if both a & c are odd or both are even. There are 25 odd numbers are 25 even numbers. Hence a and c can be selected in

S10. Ans.(b)

Sol. Given that there are 4 letters between R and E, suppose this combination R - - - - E is denoted by X, then the total number of arrangement of X and other four remaining alphabets are:

5!.2!.4! (as R and E can be permuted) 

Also, the four letters that come between R and E can be selected in 8_(C_4 ) ways. 

Required number of permutations

Important Note:

To receive the fastest updates on Bank Exams like IBPS, SBI, RBI, IPPB, etc. as well as all other ongoing as well as forthcoming exams, kindly subscribe to our website. All you have to do is enter your email in the pop-up that appears on the website when you first enter it on the home page. Once you’re subscribed, you will receive all the latest updates concerning all competitive exams.

Read More

IBPS SO Exam 2017 - Day 7 (P&C / Probability)

Dear Aspirants,

We have introduced  "the 12 days study plan to crack IBPS SO Exam 2017". This plan is specifically dedicated to Quantitative Aptitude & English Language and cover all types of questions asked in Bank SO exams. This will help you to prepare in a more efficient and systematic way. So, follow this post to keep updated with the plan.

Q1. A boy has 3 library cards and 8 books of his interest in the library. Of these 8, he does not want to borrow chemistry part II unless Chemistry part I is also borrowed. In how many ways can he choose the three books to be borrowed?

(a) 56 

(b) 27 

(c) 26

(d) 41 

(e) None of these

Q2. In how many ways can 7 persons be seated at a round table if 2 particular persons must not sit next to each other?

(a) 5040 

(b) 240 

(c) 480

(d) 720 

(e) None of these

Q3. In how many different ways can the letters of the word ‘MATHEMATICS’ be arranged so that the vowels always come together?

(a) 10080 

(b) 4989600 

(c) 120960

(d) 12960 

(e) None of these

Q4. There are 4 candidates for the post of a lecturer in Mathematics and one is to be selected by votes of 5 men. The number of ways in which the votes can be given is

(a) 24 

(b) 36 

(c) 40

(d) 48 

(e) None of these

Q5. The number of ways in which 6 men and 5 women can dine at a round table if no two women are to sit together is given by

(a) 6 ! × 5 ! 

(b) 5 ! × 4 ! 

(c) 30

(d) 7 ! × 5 ! 

(e) None of these

Q6. An urn contains 3 red and 4 green marbles. If three marbles are picked at random, what is the probability that two green and one is red?

(a) 3/7

(b) 18/35

(c) 5/14

(d) 4/21

(e) None of these

Q7. A student has 60% chance of passing in English and 54% chance of passing in both English and Mathematics. What is the percentage probability that he will fail in Mathematics?

(a) 12

(b) 36

(c) 4

(d) 10

(e) 14

Q8. When three coins are tossed together, the probability that all coins have the same face up, is

(a) 1/3

(b) 1/6

(c) 1/8

(d) 1/12

(e) 1/17

Q9. Ten identical particles are moving randomly inside a closed box. What is the probability that at any given point of time all the ten particles will be lying in the same half of the box?

(a) 1/4

(b) 1/512

(c) 2/92

(d) 2/112

(e) 1/232

Q10. 3 digits are chosen at random from 1,2,3,4,5,6,7,8 and 9 without repeating any digit. What is the probability that their product is odd?

(a) 2/3

(b) 5/108

(c) 5/42

(d) 8/42

(e) 9/42

Q11. A committee of 4 is to be formed from among 4 girls and 5 boys. What is the probability that the committee will have number of boys less than number of girls?

(a) ¼

(b) 1/5

(c) 1/6

(d) 1/7

(e) None of these

Q12. A box contains 4 black balls, 3 red balls and 5 green balls. 2 balls are drawn from the box at random. What is the probability that both the balls are of the same colour?

(a) 47/68

(b) 1/6

(c)19/66

(d)2/11

(e) None of these

Q13. In a box carrying one dozen of oranges, one-third have become bad. If 3 oranges are taken out from the box at random, what is the probability that at least one orange out of the three oranges picked up is good?

(a) 1/55

(b) 54/55

(c) 45/55

(d) 3/55

(e) None of these

Q14. A box contains 5 green, 4 yellow and 3 white marbles. 3 marbles are drawn at random. What is the probability that they are not of the same colour?

(a) 13/44

(b) 41/44

(c) 13/55

(d) 152/55

(e) None of these

Q15. Out of 15 students studying in a class, 7 are from Maharashtra, 5 from Karnataka and 3 from Goa. Four students are to be selected at random. What are the chances that at least one is from Karnataka?

(a) 12/13

(b) 11/13

(c) 100/15

(d) 51/15

(e) None of these

ANSWERS :

Important Note:

To receive the fastest updates on Bank Exams like IBPS, SBI, RBI, IPPB, etc. as well as all other ongoing as well as forthcoming exams, kindly subscribe to our website. All you have to do is enter your email in the pop-up that appears on the website when you first enter it on the home page. Once you’re subscribed, you will receive all the latest updates concerning all competitive exams.

Read More

Probability Quiz for RBI Assistant Mains / IBPS SO 2016-17

1. 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 these

2. 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 these

3. 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 these

4. 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 these

5. 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 these

6. 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 these

7. 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 these

8. 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 these

9. 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 these

10. 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 these


ANSWERS :

1. 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.

2. 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.

3. 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.

4. (4c3 + 5c3 + 6c3)/15c3 = 34/455.

5. 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.

6. 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) = 11/25

7. 1 – 22c4/30c4 = 1 – 209/783 = 574/783.

8. A selects and B rejects + B selects and A rejects = (1/5)*(5/7) + (4/5)*(2/7) = 13/35.

9. 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.

10. (8c1)/(14c1) * (8c1)*(14c1) = 16/49.

Important Note:

To receive the fastest updates on Bank Exams like IBPS, SBI, RBI, IPPB, etc. as well as all other ongoing as well as forthcoming exams, kindly subscribe to our website. All you have to do is enter your email in the pop-up that appears on the website when you first enter it on the home page. Once you’re subscribed, you will receive all the latest updates concerning all competitive exams.

Read More

Probability Quiz For All Bank Exams

1. A box contains 27 marbles some are blue and others are green. If a marble is drawn at random from the box, the probability that it is blue is 1/3. Then how many number of green marbles in the box?

A. 10
B. 15
C. 14
D. 18
E. None

Sol. Blue marble – x
xc1/27c1 = 1/3
x/27=1/3 —> x=27/3=9
No of green marbles = Total – Blue marble =27-9=18

2. In a bag there are 4 white, 4 red and 2 green balls. Two balls are drawn at random.What is the probability that at least one ball is of red colour?

A. 4/3
B. 7/3
C. 1/3
D. 2/3
E. None

Sol. Total Balls =10
Other than red ball = 6c2
6c2/10c2=1/3 —> 1-1/3 = 2/3

3. Sahil has two bags (A & B) that contain green and blue balls.In the Bag ‘A’ there are 6 green and 8 blue balls and in the Bag ‘B’ there are 6 green and 6 blue balls. One ball is drawn out from any of these two bags. What is the probability that the ball drawn is blue?

A. 15/28
B. 13/28
C. 17/28
D. 23/28
E. None

Sol. Total balls in A bag = 14, Total balls in A bag = 12
A bag = 1/2(8c1/14c1) = 2/7
B bag = 1/2(6c1/12c1) = 1/4 —> total Probability = 2/7 + 1/4 =15/28

4. In an examination, there are three sections namely Reasoning, Maths and English. Reasoning part contains 4 questions. There are 5 questions in maths section and 6 questions in English section. If three questions are selected randomly from the list of questions then what is the probability that all of them are from maths?

A. 7/91
B. 8/91
C. 2/91
D. 4/91
E. None

Sol. Total no of questions= 15
Probability = 5c3/15c3 = 2/91

5. A basket contains 5 red 4 blue 3 green marbles. If three marbles picked up random, What is the probability that either all are green or all are red ?

A. 1/20
B. 7/20
C. 3/20
D. 9/20
E. None

Sol. Total Marbles = 12
Either all are green or all are red = 5c3 + 3c3
probability = 5c3 + 3c3/12c3 = 11/220 = 1/20.

6. A basket contains 5 red 4 blue 3 green marbles. If three marbles picked up random, What is the probability that at least one is blue?

A. 41/55
B. 53/55
C. 47/55
D. 49/55
E. None

Sol. Total Marbles = 12
other than blue 8c3 / 12c3 = 14/55
probability = 1-14/55 = 41/55.

7. A basket contains 5 red 4 blue 3 green marbles. If two marbles picked up random, What is the probability that both are red?

A. 4/33
B. 5/33
C. 7/33
D. 8/33
E. None

Sol. Total Marbles = 12
Probability = 5c2 / 12c2 = 5/33.

8. A bag contains 5 red caps, 4 blue caps, 3 yellow caps and 2 green caps.If three caps are picked at random, what is the probability that two are red and one is green?

A. 22/55
B. 15/81
C. 10/91
D. 5/91
E. None

Sol. Total caps = 14
Probability = 5c2 * 2c1/ 14c3 = 5/91

9. A bag contains 5 red caps, 4 blue caps, 3 yellow caps and 2 green caps. If four caps are picked at random, what is the probability that two are red, one is blue and one is green?

A. 22/1001
B. 80/1001
C. 21/1001
D. 55/1001
E. None

Sol. Total caps = 14
Probability = 5c2 * 4c1 * 2c1 / 14c4 = 80/1001.

10. A bag contains 2 red caps, 4 blue caps, 3 yellow caps and 5 green caps. If three caps are picked at random, what is the probability that none is green?

A. 2/13
B. 3/13
C. 1/13
D. 5/13
E. None

Sol. Total caps = 14
Probability = 5c0 * 9c3/ 14c3 = 3/13.

Important Note:

To receive the fastest updates on Bank Exams like IBPS, SBI, RBI, IPPB, etc. as well as all other ongoing as well as forthcoming exams, kindly subscribe to our website. All you have to do is enter your email in the pop-up that appears on the website when you first enter it on the home page. Once you’re subscribed, you will receive all the latest updates concerning all competitive exams.

Read More