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Thursday, 23 March 2017

SBI PO Prelims Exam 2017 - Day 12 (P&C / Probability)

Dear Aspirants,

We have introduced "the 45 days study plan to crack SBI PO Prelims Exam 2017". This plan is specifically dedicated to Quantitative Aptitude, English Language & Reasoning and cover all types of questions asked in Bank PO 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. How many positive numbers can be formed by using any number of the digits 0, 1, 2, 3 and 4, no digit being repeated in any number?

(a) 360

(b) 260

(d) 280

(e) None of these

Q2. In how many ways 3 prizes can be given away to 7 boys when each boy is eligible for any of the prizes?

(a) 243

(b) 343

(d) 2187

(e) None of these

Q3. In a class of 15 students, there are 5 girls. In how many different ways can they be arranged in a row such that no two of the five girls are consecutive?

Q4. How many words can be formed with the letters of the word “Pataliputra’ without changing the relative order of the vowels and consonants?

(a) 3600

(b) 6300

(d) 4600

(e) None of these

Q5. How many different letter arrangements can be made from the letters of the word RECOVER?

(a) 1210

(b) 5040

(d) 1200

(e) None of these

Q6. In a single throw of two dice what is the probability of not getting the same number on both the dice?

(a) 1/6

(b) 2/3

(d) 1/3

(e) None of these

Q7. One card is drawn at random from a pack of 52 cards. What is the probability that the card drawn is either a red or a king?

(a) 6/13

(b) 1/2

(d) 27/52

(e) None of these

Q8. A bag contains 3 red, 5 yellow and 4 green balls. 3 balls are drawn randomly. What is the probability that the balls drawn contain balls of different colours?

(a) 4/15

(b) 3/11

(d) 5/14

(e) None of these

Q9. A bag contains 5 red, 7 yellow and 6 green balls. 3 balls are drawn randomly. What is the probability that balls drawn contain exactly 2 green balls?

(a) 14/68

(b) 13/68

(d) 15/68

(e) None of these

Q10. A bag contains 5 red, 6 yellow and 7 green balls. 3 balls are drawn randomly. What is the probability that the balls drawn contain no red ball?

(a) 55/282

(b) 55/272

(d) 143/406

(e) None of these

Q11. A box contains 4 green, 5 yellow and 4 white marbles. 3 marbles are drawn at random. What is the probability that all the three marbles are not of same colour?

(a) 9/143

(b) 134/143

(d) 135/143

(e) None of these

Q12. A bag contains 4 red and 7 black balls. Two draws of three balls each are made, the ball being replaced after the first draw. What is the chance that the balls were red in the first draw and black in the second?

(a) 28/5445

(b) 25/5448

(d) 25/4554

(e) None of these

Q13. A bag contains 9 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) 9/65

(b) 6/65

(d) 8/130

(e) None of these

Q14. A basket contains 5 white and 9 black balls. There is another basket which contains 7 white and 7 black balls. One ball is to drawn from either of the two baskets. What is the probability of drawing a white ball?

(a) 4/7

(b) 6/7

(d) 2/7

(e) None of these

Q15. 8 persons are seated at a round table. What is the probability that 3 particular persons sit together?

(a) 2/7

(b) 1/7

(d) 3/14

(e) None of these

Solutions :

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

(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

(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

(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

(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

(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

(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

(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

(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

(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

(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

(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

(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

(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

(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

(d) 2/11

(e) None of these

ANSWERS :

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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:

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

(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

(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

(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

(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 !

(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

(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

(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

(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

(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

(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

(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

(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

(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

(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

(d) 51/15

(e) None of these

ANSWERS :