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 PO MAINS 2016 - Quant Quiz-4 (P&C and Probability)

1. In how many ways "PROBATIONARY" can be written such that the vowels are always together ?

A. 2 * 7!*5!
B. 8!
C. 2 * 8!*5!
D. 8! / 2!
E. 7!

2. What is the probability that the number selected from the set {1,2,3,.......50} is a multiple of 3 or 6 ?

A. 12/25
B. 8/25
C. 4/25
D. 16/25
E. None of these

3. A bag contains 4 black and 6 white balls. 2 balls are drawn at randomn. Find the probability that atleast one of them is black ?

A. 1/3
B. 2/3
C. 3/4
D. 3/5
E. None of these

4. A bag contains 20 tickets numbered from 1-20. 2 tickets are drawn at randomn. Find the probability that both numbers are prime ?

A. 16/95
B. 15/95
C. 14/95
D. 17/95
E. None of these

5. 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. 9/40
B. 7/40
C. 11/40
D. 13/40
E. None of these

6. If 20 lines are drawn in a plane such that no two of them are parallel and no three are concurrent, the number of points in which they intersect each other is ?

A. 200
B. 180
C. 190
D. 220
E. 230

7. A boy has 3 library tickets and 8 books of his interest are there in the library. Out of these 8, he does not want to borrow Chemistry Part II, unless Chemistry Part I is also borrowed. The number of ways in which he can choose the three books to be borrowed is ?

A. 42
B. 40
C. 41
D. 45
E. 44

8. In a football championship, 153 matches were played. Every two teams played one match with each other. The number of teams, participating in the championship were ?

A. 20
B. 22
C. 16
D. 18
E. None of these

9. How many motor vehicle registration number plates can be formed with the digits 1, 2, 3, 4, 5 (no digits being repeated) if it is given that registration number can have 1 to 5 digits ?

A. 320
B. 325
C. 350
D. 315
E. None of these

10. If a team of four persons is to be selected from 8 males and 8 females, then in how many ways can the selections be made to include at least one male ?

A. 1750
B. 1500
C. 1450
D. 1600
E. None of these


                                                ANSWERS

1. Vowels in the word PROBATIONARY are O, A, I, O, A
     Now keeping them together and treating them as one word.
     No.  of ways of writting that will be = 8!
     Now the vowel group its self can be written in = (5!/2!*2!) 

Thus, total ways of writing PROBATIONARY is = (8!*5!)/(2!*2!) = 2*7!*5!

2. Multiples of 3 are {3,6,.......,48} = 16 numbers
    Multiples of 6 are {6,12,18,...48} = 8 numbers

Now, as multiples of 6 are already included in multiples of 3.
Thus, no. of favorable cases are = 16

Required Probability = 16/50 = 8/25

3. Total ways of selecting 2 balls from 10 = 10C2 = 45
     No. of ways of selecting 2 white balls from 6 white balls = 6C2 = 15

No. of favorable cases are = total ways - no. of ways of selecting no black ball or in                                                                           other words 2 white balls

                                              = 45 - 15 = 30

Required Probability = 30/45 = 2/3

4. Total prime no.s from 1-20 = 8
    Total ways of selecting 2 tickets from 20 = 20C2 = 190
     No. of ways of selecting two prime no.s from 8 = 8C2 = 28

Required Probability = 28/190 = 14/95.


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

 6.

    

    
7. Number of Ways =  No Chemistry or Chemistry I alone or Chemistry I and
                                     Chemistry II
   
    = 6C3 + 6C2 + 6C1 = 20 + 15 + 6 = 41.

8. 
    
    
     

9. If number is 1 digit number, Number of ways= 5. 

    If number is 2 digit number, Number of ways=5×4=20

    If 3 digit number, Number of ways= 5×4×3= 60

    If 4 digit number, Number of ways=5×4×3×2=120

    If 5 digit number, Number of ways=5×4×3×2×1=120.

    By adding these we get the sum as 325.

10. If we subtract the cases in which all are females, we will be left with the cases where atleast one male is selected.

     Therefore, the total ways in which 4 members can be selected from 16 = 16C4 
      and total ways in which 4 females can be selected = 8C4.
      So required ways to select at least one male is 16C4 - 8C4 = 1750.

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Answers To Probability Quiz-5

1) A
2) C
3) B
4) C
5) A
6) B

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.Probability Quiz-5 for IBPS PO

1) Prachi gives 2 exams in a day. Chances of clearing each exam are 0.45 and 0.75 respectively. Then what is the probability that she cleared atleast 1 exam ?

A. 0.9
B. 0.725
C. 0.8625
D. 0.8125

2) Ramesh wants to go to China by airplane. There are 3 flights available Jet, Indigo and Spice airlines. Then what is the probability that he chose Indigo ?

A. 1/2
B. 2/3
C. 1/3
D. 3/4

3) Two dices are rolled simulataneously. Then what is the probability even numbers on both dices ?

A. 1/12
B. 1/4
C. 1/9
D. 4/9

4) A bag contains 4 white and 3 black balls. 3 balls are drawn at randomn. What is the probability of none of the balls being black ?

A. 3/35
B. 2/35
C. 1/35
D. 4/35

5) In a society of 50 members, 10 speaks both english and hindi, 15 speak both english and punjabi and 5 speak both hindi and punjabi. There are 5 members who speak all 3 languages. Then what is the probability of choosing a member who speaks only one of the languages ?

A. 3/10
B. 2/5
C. 1/5
D. 1/10

6) From a set of first 50 natural numbers, 2 numbers are chosen at randomn. Then what is the probability that one of them is a multiple of 5 and other is a multiple of 3 ?

A. 16/245
B. 32/245
C. 9/245
D. 62/245

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Answers To Probability Quiz-4

1) C
2) C
3) D
4) A
5) C
6) C

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Probability Quiz-4 for IBPS PO

1) Sahil orders a gift for his wife Neeti for diwali. Due to festival season there is a chance of delay, so playing it safe he orders from 3 retailers A, B and C which have probability of reaching on time as 0.8, 0.9 and 0.6. Then what is the probability that he got the gift on time ?

A. 0.882
B. 0.9
C. 0.992
D. 0.772

2) A box contains 4 black, 4 green and 2 red balls. 2 balls are drawn at randomn. What is the probability of getting atleast 1 red ball ?

A. 1/5
B. 19/45
C. 17/45
D. 2/5

3) Prabhas is travelling from shimla to manali. Due to bad weather some routes are blocked. There are 3 routes to reach manali with the probability of reaching, for 'A'=0.7, 'B'=0.6 and
'C'=0.5. Find the probability of reaching if 'C' was not chosen ?

A. 0.6
B. 0.7
C. 0.56
D. 0.65

4) A set of numbers { 2, 4, 6, 8, 9 } belongs to 'x'. Then what is the probability of the function f(x)=(x-3)/(x-4) being defined on these set of values ?

A. 4/5
B. 2/5
C. 1/5
D. 3/5

5) A bag contains different types of chocolates. 3 milky bar, 4 mars and 5 bounty. 2 chocolates are drawn at randomn without repetition. Then what is the probability of getting atleast 1 bounty ?

A. 5/11
B. 5/22
C. 15/22
D. 7/22

6) A deck of 52 cards is well shuffled. Now a card is drawn at randomn from it. Then what is the probability of drawing a face card or a black color card ?

A. 4/13
B. 21/26
C. 9/13
D. 4/9

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Answers To Probability Quiz-3

1) D
2) C
3) C
4) C
5) C
6) C

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Probability Quiz-3 for IBPS PO

1) X contains { 2, 3, 4, 5, 6 } as its elements then probability of modulus (X-3) < 2 ?

A. 2/5
B. 1/5
C. 4/5
D. 3/5

2) In an examination, 'A' s probability of passing is 0.4 and 'B's probability of passing is 0.6 . Then what is the probability of atleast one of them passing ?

A. 0.8
B. 0.75
C. 0.84
D. 0.9

3) Two digit numbers are formed using { 0, 2, 3, 4, 5 } then what is the probability of the 2 digit number being divisible by 2 or 5 ?

A. 3/4
B. 11/16
C. 13/16
D. 7/16

4) There are 2 jars, one contains 2 white, 3 black balls and other jar contains 3 white, 2 black balls then if 3 balls are drawn one of the jar then what is the probability of 2 being black and 1 being white ?

A. 9/10
B. 7/10
C. 9/20
D. 7/20

5) A committee  of 3 persons has to be formed from 4 women and 3 men. Then what is the probability of having atleast one woman in the committee ?

A. 16/35
B. 29/35
C. 34/35
D. 24/35

6) In a class of 100 students, 20 like both maths and physics, 10 like both physics and biology and 5 like both maths and biology. There are 50 students who like only one subject. Then probability of choosing a student who likes all 3 subjects ?

A. 1/4
B. 1/5
C. 3/20
D. 3/10 

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Answers To Probability Quiz-2

1) C
2) A
3) C
4) B
5) B
6) B

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Probability Quiz-2 for IBPS PO

1) Two cards are drawn from a deck of 52 cards one after another without replacement. What is the probability that atleast one of the card is black ?

A. 1/2
B. 23/102
C. 25/102
D. 1/4

2) Out of 200 students in a class, 100 play cricket, 50 play hockey and 60 play basketball. 30 play both cricket and hockey, 45 play both cricket and basketball and 35 play both hockey and basketball. If one student is chosen at randomn  from the class, then what is the maximum probability that he/she plays all the game ?

A. 3/20
B. 3/10
C. 1/10
D. 1/5

3) Out of 200 students in a class, 100 play cricket, 50 play hockey and 60 play basketball. 30 play both cricket and hockey, 45 play both cricket and basketball and 35 play both hockey and basketball. If one student is chosen at randomn  from the class, then what is the minimum probability that he/she plays all the game ?

A. 3/20
B. 3/10
C. 1/10
D. 1/5

4) The domain of the function f(x) consists of { 1, 2, 3, 4, 5, 6 } then what is the probability of f(x)< 8 where f(x)= 2x-1 ?

A. 1/2
B. 2/3
C. 5/6
D. 1/3

5) A card is drawn from a deck of 52 cards. Then what is the probability of it being an ace given that its black ?

A. 1/13
B. 1/2
C. 2/13
D. 1/3

6) A bag contains 2 white, 3 black and 4 blue balls. 3 balls are drawn one after another without replacement. Then what is the probability of not getting any white ball ?

A. 343/729
B. 5/12
C. 7/9
D. 7/12

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Answers To Probability Quiz-1

1) A
2) A
3) C
4) C
5) D
6) B

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Probability Quiz-1 for IBPS PO

1) A basket contains 3 mangoes, 2 apples and 1 orange. Then what is the probability of choosing either an apple or an orange ?

A. 1/2
B. 1/3
C. 2/3
D. 3/4

2) There are 3 types of balls ( Cricket ball, Football and Tennis ball) i.e. 2 Cricket balls, 2 Footballs and 2 Tennis balls. If any 2 balls are placed in each of the 3 boxes, then what is the probability of selected box containing atleast 1 Cricket ball ?

A. 1/2
B. 2/3
C. 1/4
D. 1/6

3) A box contains 3 red , 4 green and 2 yellow pens. 2 pens are drawn at randomn. Wht is the probability of drawing pens of the same color ? 

A. 1/3
B. 2/3
C. 5/18
D. 13/18

4) Two dices are thrown simultaneously. What is the probability that the sum of the numbers on dices is a prime number ?

A. 11/18
B. 15/36
C. 7/18
D. 4/9

5) Both Suresh and Ramesh gave IBPS exam. The probability of clearing the exam for Suresh is 2/5 and for Ramesh is 3/4. What is the probability that neither of them clears the exam ?

A. 3/10
B. 7/10
C. 7/20
D.3/20

6) 'A' and 'B' both plays a game where you have to clear the previous round t get to the next round. There are 2 rounds to clear the game. The probability of clearing both rounds are same for 'A' which is 0.65 and same goes for 'B' its probability is 0.45. Then what is the probability that only one of them cleared the game ?

A. 0.40
B. 0.45
C. 0.50
D. 0.42

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