Dear Aspirants, Our IBPS Guide team is providing new series of Quants Questions for SBI Clerk/ IBPS Clerk Prelims so the aspirants can practice it on a daily basis. These questions are framed by our skilled experts after understanding your needs thoroughly. Aspirants can practice these new series questions daily to familiarize with the exact exam pattern and make your preparation effective.
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1) A box contains 3 red, 4 yellow and (x + 1) green balls. If two balls are taken out, then the probability that both the balls being green is 5/33. Find the value of x?
A.3
B.4
C.2
D.1
E.5
2) A box contains three red, four yellow and one green balls. If three balls are drawn at random, what is the probability that two of them are red and one green?
A.1/56
B.1/28
C.3/56
D.1/14
E.5/56
3) A bag contains 5 red and x yellow balls. If two balls are drawn at random, then the probability of that balls being red is 5/33. Find the value of x.
A.5
B.3
C.7
D.8
E.2
4) A bag contains 12 blue balls, 7 white balls and 6 yellow balls. If 2 balls are drawn at random, then find the probability of getting all the balls are same in colour?
A.21/50
B.17/50
C.31/50
D.19/50
E.None of these
5) A bag contains 3 red, 5 yellow and 4 blue balls. If three balls are drawn at random, then find the probability of that balls are yellow?
A.1/22
B.1/11
C.3/22
D.2/11
E.5/22
6) Ratio of the number of red, blue and black pens in a box is 2:1:3 respectively and the average number of pens in the box is 6. If two pens are drawn at random, then find the probability of getting all the pens are in same color?
A.1/17
B.5/18
C.6/17
D.7/18
E.None of these
7) Box A contains 2x red balls, (x + 3) pink balls and x violet balls. If one ball is drawn from the box and the probability of that ball being pink is 2/5, then find the value of x?
A.5
B.4
C.1
D.2
E.3
8) In a bag, the average number of red and black balls is 18. If one ball is taken out at random and the probability of getting a red ball is 7/12, then find the number of black balls in the bag?
A.21 balls
B.15 balls
C.12 balls
D.18 balls
E.None of these
9) A box contains 5 apples and 7 Oranges. If three fruits are drawn in the box without replacement, then what is the probability that the first fruit is apple, second is Orange and third is apple?
A.5/108
B.7/108
C.5/216
D.21/216
E.None of these
10) A bag contains 3 red, 2 blue and 4 green balls. 2 balls are drawn randomly from the bag. Find the probability that out of 2 balls at least one ball is blue?
A.5/36
B.5/12
C.1/2
D.7/12
E.None of these
Answers :
1) Answer: B
(x + 1)C2/ (8+ x)C2Â = 5/33
5 * (8 + x) * (7 + x) = 33 * (x + 1) * x
5 * (56 + 8x + 7x + x2) = 33x2Â + 33x
280 + 75x + 5x2Â = 33x2Â + 33x
28x2 – 42x – 280 = 0
2x2Â -3x-20= 0
x=4,-5/2
So, the value of x= 4
2) Answer: C
Required probability = (3C2Â * 1C1)/8C3
= 3/56
3) Answer: C
5C2/(5 + x)C2Â = 5/33
(5 + x) * (4 + x) = 4 * 33
20 + 5x + 4x + x2Â = 132
x2 + 9x – 112 = 0
x2 + 16x – 7x – 112 = 0
x(x + 16) – 7(x + 16) = 0
x = 7
4) Answer: B
Required probability=(12C2+7C2+6C2)/25C2
=(66+21+15)/300=102/300
=17/50
5) Answer: A
Required probability = 5C3/12C3
= 5 * 4 * 3/12 * 11 * 10
= 1/22
6) Answer: C
Total number of pens=6*3=18 pens
Red pens=18*2/6=6 pens
Blue pens=18*1/6=3 pens
Black pens=18*3/6=9 pens
Required probability=(6C2+3C2+9C2)/18C2
=(15+3+36)/153
=54/153
=6/17
7) Answer: E
(x + 3)C1/(2x + x + 3 + x)C1Â = 2/5
8x + 6 = 5x + 15
3x = 9
x = 3
8) Answer: B
Total number of balls (red+black)=18*2=36
Probability of getting a red ball=7/12
x/36=7/12
x=21
Number of black balls=36-21=15 balls
9) Answer: E
Required probability = 5/12 * 7/11 * 4/10
= 7/66
10) Answer: B
Required probability = 7C1Â * 2C1/9C2Â + 2C2/9C2
= (14 + 1)/36
= 15/36
= 5/12
Start Quiz
11) A box contains the 5 red balls, 3 pink balls and x black balls. If two balls is drawn at random and probability of both balls being red is 2/9, then find the value of x?
A.3
B.5
C.4
D.2
E.None of these
12) The box contains three Red balls, four Green balls and five Blue balls. If two balls are drawn from the box, what is the probability of both the balls are of same color?
A.19/66
B.17/66
C.13/66
D.37/66
E.None of these
13) A box contains 5 red balls, 2 white balls, 6 black balls. If two balls are drawn at random, then find the probability that both balls are either red or black balls?
A.25/78
B.12/35
C.3/26
D.13/35
E.None of these
14) A bag contains 4 white, 5 red and 7 yellow balls. Three balls are drawn from the bag at random, then what is the probability that all the balls are red?
A.1/61
B.1/35
C.1/45
D.1/56
E.None of these
15) A bag contains 3 Red, 4 Green and 5 Blue balls. If two balls are drawn at random, then what is the probability that balls are either Red or Blue?
A.13/55
B.12/55
C.13/66
D.17/66
E.5/22
16) What is the probability of forming four members committee from 5 men and 4 women with at least one woman member in committee?
A.121/126
B.61/63
C.104/125
D.125/126
E.None of these
17) A bag contains 5 white, 6 black and 7 blue balls. If four balls are drawn at random, find the probability that 2 are white and 2 are blue balls.
A.7/102
B.10/101
C.5/102
D.4/103
E.None of these
18) A box contains 4 white and 8 yellow balls. Two balls are taken out at random without replacement. If the first ball is white, then what is the probability that the second ball is also white?
A.1/11
B.3/11
C.5/11
D.4/11
E.None of these
19) A first bag contains 3 white and 4 black balls. A second bag contains 3 white and 2 black balls. One bag is selected at random and from the selected bag one ball is drawn, then find the probability that the ball is white.
A.6/7
B.12/13
C.18/35
D.5/6
E.None of these
20) There are 10 boys and 5 girls in a class. Five students are selected at random. What is the probability that 3 girls and 2 boys are selected?
A.150/1001
B.45/89
C.1001/150
D.89/789
E.None of these
Answers :
11) Answer: D
5C2/(8 + x)C2Â = 2/9
20 * 9 = 2 * (8 + x) * (7 + x)
90 = 56 + 8x + 7x + x2
x2 + 15x – 34 = 0
x2 + 17x – 2x – 34 = 0
x(x + 17) – 2(x + 17) = 0
(x – 2)(x + 17) = 0
x = 2, -17
12) Answer: A
n(E) = (3C2Â + 4C2Â + 5C2)/12C2
= (3 * 2 + 4 * 3 + 5 * 4)/(12 * 11)
= 38/132
= 19/66
13) Answer: A
P(E) = n(E)/n(S)
Total probability = n(S) =Â 13C2
The probability that both balls are either red or black balls
n(E) = 5C2 or 6C2
P(E) = (5C2 or 6C2)/13C2
P(E) = (10 + 15)/78
P(E) = 25/78
14) Answer: D
Total balls = 4 + 5 + 7 = 16
Required probability =Â 5C3Â /Â 16C3Â = (3 * 4 * 5)/(16 * 15 * 14) = 1/56
15) Answer: C
Required probability = (3C2Â + 5C2)/12C2
= 13/66
16) Answer: A
Committee of 4 members with at least one woman (i.e. min. 1 woman max. 4)
(1w & 3m) or (2w & 2m) or (3w & 1m) or (4w & 0m)
= (4C1 × 5C3) + (4C2 × 5C2) + (4C3×5C1) + (4C4×5C0)
= 40 + 60 + 20 + 1 = 121
4 members selected from 9 members,
9C4Â = 126
Therefore, required Prob. = 121/126
17) Answer: A
Total balls = 5 + 6 + 7 = 18
Required probability = (5C2Â *Â 7C2)/18C4Â = 7/102
18) Answer: A
Number of white balls = 4, Number of yellow balls = 8
Number of balls taken out at random = 2
Total balls = 4 + 8 = 12
Required probability = 4/12 * 3/11 = 1/11
19) Answer: C
Probability of selecting a bag = ½
Probability of getting white ball from first bag = 3/7
Probability of getting white ball from second bag = 3/5
Required probability = ½ * 3/7 + ½ * 3/5 = 3/14 + 3/10 = 18/35
20) Answer: A
Required probability = (5C3Â *Â 10C2)/Â 15C5Â = 150/1001
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