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Probability - MCQ 4 - Bank Exams MCQ

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20 Questions MCQ Test - Probability - MCQ 4

Probability - MCQ 4 for Bank Exams 2024 is part of Bank Exams preparation. The Probability - MCQ 4 questions and answers have been prepared according to the Bank Exams exam syllabus.The Probability - MCQ 4 MCQs are made for Bank Exams 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Probability - MCQ 4 below.

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Probability - MCQ 4 - Question 1

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A box contain 4 white, 3 blue and 2 black marbles. If 2 marbles are picked up at random. What is the probability that both of them are black ?

A.
20
B.
1/36
C.
1/22
D.
36
E.
None of these

Detailed Solution for Probability - MCQ 4 - Question 1

P = 2C2/9C2 = 1/36

Probability - MCQ 4 - Question 2

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An urn contains 6 maroon, 3 pink and 4 white balls. If three balls are drawn What is the probability that all are pink or white?

A.
11/328
B.
7/212
C.
5/286
D.
9/127
E.
None of these

Detailed Solution for Probability - MCQ 4 - Question 2

P =3C3/13C3 + 4C3/13C3
= 1/286 + 4/286 = 5/286

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Probability - MCQ 4 - Question 3

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From a pack of 52 cards 3 cards are drawn one by one without replacements.Find the probability that both of them are king ?

A.
132/1338
B.
32/2340
C.
1/5525
D.
4/2755
E.
None of these

Detailed Solution for Probability - MCQ 4 - Question 3

4/52*3/51*2/50 = 24/132600 = 4/22100 = 1/5525

Probability - MCQ 4 - Question 4

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If two dice are thrown simultaneously, what is the probability that the sum of the numbers appeared is less than seven?

A.
5/12
B.
7/12
C.
6/17
D.
13/27
E.
None of these

Detailed Solution for Probability - MCQ 4 - Question 4

Sum of the numbers can be 1,2, 3, 4, 5, and 6.
1+2= 3
1+3 = 4
1+4 = 5
1+5 = 6
2+3 = 5
3+2 = 5
2+4 = 6
4+2 = 6……..etc
n (E) = 15, n (S) = 36
P (E) =15/36 = 5/12

Probability - MCQ 4 - Question 5

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A box contains 5 white, 4 green, 2 blue and 3 black marbles. If 2 marbles are drawn at random, what is the probability that both are green or at least one is green ?

A.
46/91
B.
32/97
C.
16/75
D.
1/54
E.
None of these

Detailed Solution for Probability - MCQ 4 - Question 5

4C2+(4C1*10C1)/12C2 = 6+40/91 = 46/91

Probability - MCQ 4 - Question 6

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In a shelf, there are 7 Banking awareness, 6 English and 5 GK books. One book is picked up randomly. What is the probability that it is neither in Banking awareness nor in GK ?

A.
1/13
B.
2/17
C.
1/3
D.
12/27
E.
None of these

Detailed Solution for Probability - MCQ 4 - Question 6

P = 6/18 = 1/3

Probability - MCQ 4 - Question 7

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A suitcase contains 4 blue shirts, 5 red shirts and 3 white shirts.If 4 shirts are drawn what is the probability that exactly one of them is blue ?

A.
113/218
B.
14/167
C.
123/234
D.
224/495
E.
None of these

Detailed Solution for Probability - MCQ 4 - Question 7

P = 4C1*8C3/12C4 = 4*56/495 = 224/495

Probability - MCQ 4 - Question 8

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A bag contains 4 white, 8 black and 6 blue balls. If two balls are drawn at random, find the probability of both the balls being black?

A.
22/137
B.
14/123
C.
28/253
D.
7/105
E.
None of these

Detailed Solution for Probability - MCQ 4 - Question 8

n(S) = 18C2 = 153
There are eight black balls, out of which two balls are drawn in 8C2 ways.
n(E) = 28
P(E) = 28 /153 = 28/153

Probability - MCQ 4 - Question 9

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The ratio of the number of girls to the number of boys is the 5 : 2 in a class of 21 students. A group of three students is to to be selected at random amongst them. What is the probability that the selected group of students contain one boy and two girls?

A.
45/266
B.
32/343
C.
120/217
D.
46/267
E.
None of these

Detailed Solution for Probability - MCQ 4 - Question 9

5:2 = 15+6 = 21
n(S) = 21C3 = 1330
n(E) = 15C1 × 6C2 = 15 × 15 = 225
P = 225/1330 = 45/266

Probability - MCQ 4 - Question 10

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A bag 5 red and 8 white balls.Two draws of three balls each are made.What is the probability that the balls were pink in the first draw and white in the second draw ?

A.
23/345
B.
140/20449
C.
20440/110
D.
230/23454
E.
None of these

Detailed Solution for Probability - MCQ 4 - Question 10

5C3/13C3 *8C3/13C3 = 60/286*56/286 = 140/20449

Probability - MCQ 4 - Question 11

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From a pack of 52 cads, 2 cards are drawn at random. What is the probability of drawing such that there is at least 1 king?

A.
35/256
B.
33/220
C.
33/221
D.
23/190
E.
11/221

Detailed Solution for Probability - MCQ 4 - Question 11

Case 1: 1 is king
⁴C₁ * ⁴⁸C₁ / ⁵²C₂
Case 2: both are king
⁴C₂ / ⁵²C₂
Add both cases.

Probability - MCQ 4 - Question 12

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A box contains 6 blue, 5 green and 4 red balls. If two balls are pick at random, then what is the probability that neither is blue?

A.
10/21
B.
12/35
C.
3/5
D.
11/21
E.
None of these

Detailed Solution for Probability - MCQ 4 - Question 12

Total balls = 15
Not blue means green or red i.e. any of (5+4) = 9 balls
So prob. = ⁹C₂ / ¹⁵C₂

Probability - MCQ 4 - Question 13

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A box contains 5 blue and 5 white balls. What is the probability of drawing 2 balls such that both are same in color?

A.
4/9
B.
4/7
C.
1/5
D.
7/12
E.
3/10

Detailed Solution for Probability - MCQ 4 - Question 13

Case 1: Both blue
⁵C₂ / ¹⁰C₂
Case 2: Both white
⁵C₂ / ¹⁰C₂
Add both cases

Probability - MCQ 4 - Question 14

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A committee of 4 people is to be formed from 3 men, 2 women and 4 children. What is the probability that exactly two of chosen people are children?

A.
13/21
B.
10/31
C.
5/21
D.
10/21
E.
None of these

Detailed Solution for Probability - MCQ 4 - Question 14

2 children should be there and rest 2 either from (2 women + 3 men) 5 people
So prob. = ⁴C₂ * ⁵C₂ / ⁹C₄

Probability - MCQ 4 - Question 15

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In a class 30% of the students opt for Math, 20% opt for Computers and 10% opt for both. A student is selected at random, find the probability that he has opted either Math or Computers.

A.
3/5
B.
2/5
C.
4/9
D.
6/11
E.
None of these

Detailed Solution for Probability - MCQ 4 - Question 15

Prob. of math = 30/100 = 3/10, Prob. of computers = 20/100 = 1/5, prob. for both = 10/100 = 1/10
So required prob. = 3/5 + 1/5 – 1/10

Probability - MCQ 4 - Question 16

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From a pack of 52 cards, 2 cards are drawn at random. What is the probability that either both are red or both are kings?

A.
55/221
B.
52/225
C.
44/221
D.
48/221
E.
None of these

Detailed Solution for Probability - MCQ 4 - Question 16

Prob. of both red = ²⁶C₂ / ⁵²C₂
Prob. of both kings = ⁴C₂ / ⁵²C₂
Since there are also cads which are both red and king, so we will subtract there prob.
There are 2 red cards which are kings
Prob. of both red and king = ²C₂ / ⁵²C₂
So required prob. = ²⁶C₂ / ⁵²C₂ + ⁴C₂ / ⁵²C₂ – ²C₂ / ⁵²C₂

Probability - MCQ 4 - Question 17

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A box contains 10 electric bulbs from which 2 bulbs are defective. Two bulbs are chosen at random. What is the probability that one of them is defective?

A.
3/10
B.
16/45
C.
25/68
D.
8/33
E.
9/19

Probability - MCQ 4 - Question 18

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A bag contains 8 blue and 7 green balls. A ball is drawn out of it and put back in the bag. Then a ball is drawn again. What is the probability that both the balls are green?

A.
36/225
B.
48/221
C.
49/225
D.
40/221
E.
None of these

Probability - MCQ 4 - Question 19

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A bag contains 8 blue and 7 green balls. 2 balls are drawn one by one without replacement. What is the probability that the balls are alternately of different colors?

A.
9/21
B.
8/17
C.
5/14
D.
8/15
E.
9/19

Detailed Solution for Probability - MCQ 4 - Question 19

When 1st is blue, prob. = 8/15 * 7/14
When 1st is green, prob. = 7/15 * 8/14
Add both cases.

Probability - MCQ 4 - Question 20

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There are 5 men and 3 women. A committee of 3 members is to be made. Find the probability that either there are 2 men and 1 woman or 2 women and 1 man.

A.
5/51
B.
45/56
C.
35/51
D.
48/61
E.
None of these

Detailed Solution for Probability - MCQ 4 - Question 20

2 men and 1 woman, prob. = ⁵C₂ * ³C₁ / ⁸C₃
2 women and 1 man, prob. = ⁵C₁ * ³C₂ / ⁸C₃
Add both cases

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