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

(c) 620 

(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

(c) 433

(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

(c) 3900

(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

(c) 1260

(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

(c)  5/6

(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

(c)  7/13

(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

(c)  1/12

(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

(c)  15/91

(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

(c)  143/408

(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

(c)  8/143

(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

(c)  28/4554

(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

(c)  9/130

(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

(c)  3/7

(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

(c)  3/14

(d)  3/14

(e) None of these

Solutions :

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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 :

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IPPB Scale-1 Officer Prelims 2017 - Day 9 (P&C / Probability)

Dear Aspirants,

We have introduced  "the 17 days study plan to crack IPPB Scale-1 Prelims 2017". This plan is specifically dedicated to Quantitative Aptitude 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.

1. Find the probability that a number from 1 to 300 is divisible by 3 or 7 ?

A. 37/75
B. 32/75
C. 36/75
D. 28/75
E. 26/75

Sol. Between 1 and 300 there are 100 multiples of 3
and 42 multiples of 7, while 14 are common multiples of 3 and 7
So total no. of favourable cases = 100 + 42 − 14 = 128.
Required probability = 128/300 = 32/75.

2. There are 3 red balls, 4 blue balls and 5 white balls. 2 balls are chosen randomly. Find probability that 1 is red and the other is white ?

A. 5/22
B. 5/23
C. 7/22
D. 4/9
E. None of these

Sol. Required Probability = (3c1 × 5c1)/12c2 = 5/22.

Directions (3-5): Study the following information carefully to answer the questions that follow :

A box contains 2 blue caps, 4 red caps, 5 green caps and 1 yellow cap.

3. If one cap is picked at random, what is the probability that it is either blue or yellow ?

A. 2/9
B. 1/4
C. 3/8
D. 6/11
E. None of these

Sol. Required Probability = (2c1 + 1c1)/12c1 = 3/12 = 1/4.

4. If two caps are picked at random, what is the probability that at least one is red ?

A. 1/3
B. 16/21
C. 19/33
D. 7/19
E. None of these

Sol. Required Probability = (4c1×8c1 + 4c2)/12c2 = (38×2)/(12×11) = 19/33.

5. If three caps are picked at random, what is the probability that two are red and one is green ?

A. 9/22
B. 6/19
C. 1/6
D. 3/22
E. None of these

Sol. Required Probability = (4c2×5c1)/12c3 = 3/22.

6. Find the number of ways of distributing 8 identical balls into 3 boxes so that no box is empty and each box being large enough to accommodate all balls ?

A. 24
B. 28
C. 36
D. 21
E. 18

Sol. (8-1)C(3-1) = 7C2 = 7×6/2×1 = 21.

7. A group consists of 4 couples  in which each of the 4 men have one wife each. In how many ways could they arranged in a straight line so that the men and women occupy alternate position ?

A. 576
B. 982
C. 1152
D. 1024
E. None of these

Sol. 4!×4! + 4!×4! = 576+576 = 1152.

8. A five digit number is formed with the digits 0,1,2,3 and 4 without repetition.Find the chance that the number is divisible by 2 ?

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

Sol. 5 digit number = 5! = 120
Divisible by 2 then the last digit should be 0, 2, 4
Then no. of cases with 0 as last digit = 4! = 24
     no. of cases with 2 as last digit = 18
     no. of cases with 4 as last digit = 18
Total cases = 24 + 18 + 18 = 60
P = 60/120 = 1/2.

9. From a group of 4 men and 3 women , 2 persons are selected at random. Find the probability that at least one woman is selected ?

A. 2/3
B. 3/5
C. 5/7
D. 1/3
E. 1/2

Sol. Total cases = 7c2 = 7!/5!×2! = 21
     Cases when no women is selectd = 4c2 = 4!/2!×2! = 6
     Cases when atleast 1 woman is selected = (21-6) = 15
     Probability = 15/21 = 5/7.

10. 16 persons are participated in a party. In how many different ways can they host the seat in a circular table, if the 2 particular persons are to be seated on either side of the host ?

A. 16! × 2
B. 14! × 2
C. 18! × 2
D. 14!
E. None of these

Sol. (16 – 2)! × 2 = 14! × 2.

11. A bag contains 8 white and 9 black balls. Balls are drawn one by one. Two balls are drawn without replacement. What is the probability that one is white and other is black?

A. 8/15
B. 1/17
C. 8/17
D. 1/15
E. 9/17

Sol. Required Probability = (8C1×9C1)/(17C2) = 8/17.

12. A bag contains 3 red, 6 white and 7 black balls. Two balls are drawn at random. What is the probability that both are black ?

A. 5/40
B. 6/40
C. 7/40
D. 8/40
E. None of these

Sol. The reqd. probability is 7C2 / 16C2 = 7/40. 


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