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Probability - MCQ 3 - Bank Exams MCQ

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20 Questions MCQ Test - Probability - MCQ 3

Probability - MCQ 3 for Bank Exams 2024 is part of Bank Exams preparation. The Probability - MCQ 3 questions and answers have been prepared according to the Bank Exams exam syllabus.The Probability - MCQ 3 MCQs are made for Bank Exams 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Probability - MCQ 3 below.

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Probability - MCQ 3 - Question 1

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When two coins are tossed simultaneously, what are the chances of getting at least one tail?

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

Probability - MCQ 3 - Question 2

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A bag contains 3 red balls and 8 blacks ball and another bag contains 5 red balls and 7 blacks balls, one ball is drawn at random from either of the bag, find the probability that the ball is red.

A.
93/264
B.
95/264
C.
91/264
D.
97/264
E.
None of these

Detailed Solution for Probability - MCQ 3 - Question 2

Probability = probability of selecting the bag and probability of selecting red ball
(1/2)*(3/11) + (1/2)*(5/12) = 91/264

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Probability - MCQ 3 - Question 3

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12 persons are seated at a circular table. Find the probability that 3 particular persons always seated together.

A.
9/55
B.
7/55
C.
4/55
D.
3/55
E.
None of these

Detailed Solution for Probability - MCQ 3 - Question 3

total probability = (12-1)! = 11!
Desired probability = (10 – 1)! = 9!
So, p = (9! *3!) /11! = 3/55

Probability - MCQ 3 - Question 4

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P and Q are two friends standing in a circular arrangement with 10 more people. Find the probability that exactly 3 persons are seated between P and Q.

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

Detailed Solution for Probability - MCQ 3 - Question 4

Fix P at one point then number of places where B can be seated is 11.
Now, exactly three persons can be seated between P and Q, so only two places where Q can be seated. So, p = 2/11

Probability - MCQ 3 - Question 5

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A basket contains 5 black and 8 yellow balls. Four balls are drawn at random and not replaced. What is the probability that they are of different colours alternatively.

A.
56/429
B.
57/429
C.
61/429
D.
68/429
E.
None of these

Detailed Solution for Probability - MCQ 3 - Question 5

sol⇒ BYBY + YBYB = (5/13)*(8/12)*(4/11)*(7/10) + (8/13)*(5/12)*(7/11)*(4/10)
= 56/429

Probability - MCQ 3 - Question 6

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Direction(Q6 – Q8):

A bag contains 6 red balls and 8 green balls. Two balls are drawn at random one after one with replacement. What is the probability that

Both the balls are green

A.
13/49
B.
15/49
C.
16/49
D.
17/49
E.
None of these

Detailed Solution for Probability - MCQ 3 - Question 6

P = (8/14)*(8/14)

Probability - MCQ 3 - Question 7

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A bag contains 6 red balls and 8 green balls. Two balls are drawn at random one after one with replacement. What is the probability that

First one is green and second one is red

A.
16/49
B.
14/49
C.
11/49
D.
12/49
E.
None of these

Detailed Solution for Probability - MCQ 3 - Question 7

P = (8/14)*(6/14)

Probability - MCQ 3 - Question 8

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A bag contains 6 red balls and 8 green balls. Two balls are drawn at random one after one with replacement. What is the probability that

Both the balls are red

A.
14/49
B.
9/49
C.
11/49
D.
12/49
E.
None of these

Detailed Solution for Probability - MCQ 3 - Question 8

P = (6/14)*(6/14)

Probability - MCQ 3 - Question 9

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Find the probability that in a leap year, the numbers of Mondays are 53?

A.
1/7
B.
2/7
C.
3/7
D.
4/7
E.
None of these

Detailed Solution for Probability - MCQ 3 - Question 9

In a leap year there are 52 complete weeks i.e. 364 days and 2 more days. These 2 days can be SM, MT, TW, WT, TF, FS, and SS.
So P = 2/7

Probability - MCQ 3 - Question 10

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A urn contains 4 red balls, 5 green balls and 6 white balls, if one ball is drawn at random, find the probability that it is neither red nor white.

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

Detailed Solution for Probability - MCQ 3 - Question 10

5c1/15c1 = 1/3

Probability - MCQ 3 - Question 11

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A box contains tickets numbered from 1 to 24. 3 tickets are to be chosen to give 3 prizes. What is the probability that at least 2 tickets contain a number which is multiple of 3?

A.
35/256
B.
33/220
C.
63/253
D.
43/190
E.
59/253

Detailed Solution for Probability - MCQ 3 - Question 11

From 1 to 24, there are 8 numbers which are multiple of 3
Case 1: 2 are multiple of 3, and one any other number from (24-8) = 16 tickets
⁸C₂ * ¹⁶C₁ / ²⁴C₃ = 56/253
Case 2: all are multiples of 3.
⁸C₃ / ²⁴C₃ = 7/253
Add both cases.

Probability - MCQ 3 - Question 12

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A box contains 6 blue, 5 green and 4 red balls. Two balls are drawn at random. What is the probability that there is no red ball?

A.
3/30
B.
11/21
C.
5/18
D.
11/23
E.
None of these

Detailed Solution for Probability - MCQ 3 - Question 12

Total balls = 15
Not red means green or blue i.e. any of (5+6) = 11 balls
So prob. = ¹¹C₂ / ¹⁵C₂

Probability - MCQ 3 - Question 13

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From a pack of 52 cards, 2 cards are drawn at random. What is the probability that both cards are black card or heart card?

A.
31/102
B.
21/73
C.
1/5
D.
17/100
E.
3/10

Detailed Solution for Probability - MCQ 3 - Question 13

Prob. of black card:
²⁶C₂ / ⁵²C₂ = 25/102
Prob. of heart card:
¹³C₂ / ⁵²C₂ = 3/51
Add both cases.

Probability - MCQ 3 - Question 14

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Two cards are drawn at random from a pack of 52 cards. What is the probability that either both are black or both are jacks?

A.
62/221
B.
21/312
C.
5/21
D.
55/221
E.
None of these

Detailed Solution for Probability - MCQ 3 - Question 14

There are total 26 cards black, and 4 jacks in which 2 are black jacks
So case 1: both are black
²⁶C₂ / ⁵²C₂
case 2: both are jack
⁴C₂ / ⁵²C₂
Add both cases.
But now 2 black jacks have been added in both cases, so subtracting their prob. :
²C₂ / ⁵²C₂
So 325/1326 + 6/1326 – 1/1326

Probability - MCQ 3 - Question 15

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From a group of 3 men, 4 women and 2 children, 4 people are to be chosen to form a committee. What is the probability that the committee contains 1 each of men, women and children?

A.
4/15
B.
12/21
C.
4/19
D.
11/31
E.
None of these

Detailed Solution for Probability - MCQ 3 - Question 15

Case 1: Prob. when 2 men, 1 woman and 1 child
³C₂ * ⁴C₁ * ²C₁ / ⁹C₄ = 4/21
Case 2: Prob. when 1 man, 2 women and 1 child
³C₁ * ⁴C₁ * ²C₁ / ⁹C₄ = 2/7
Case 3: Prob. when 1 man, 1 woman and 2 children
³C₁ * ⁴C₁ * ²C₂ / ⁹C₄ = 2/21

Probability - MCQ 3 - Question 16

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A box contains 25 bulbs out of which 5 are defective. 3 bulbs are to be delivered to a customer. What is the probability that he get one defective bulb?

A.
19/46
B.
25/51
C.
44/77
D.
21/46
E.
None of these

Probability - MCQ 3 - Question 17

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There are 4 red balls, 5 white and 3 green balls in a basket. 3 balls are chosen at random. What is the probability that there is at most 1 green ball?

A.
13/40
B.
48/55
C.
25/68
D.
8/33
E.
9/19

Detailed Solution for Probability - MCQ 3 - Question 17

Case 1: 0 green ball means all three red or white balls
⁹C₃ / ¹²C₃
Case 2: 1 green ball and two red or white balls
⁹C₂ * ³C₁ / ¹²C₃ Add both cases.

Probability - MCQ 3 - Question 18

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A bag contains 3 red, 4 green and 3 yellow balls. If 2 balls are drawn at random, what is the probability that they are of different color?

A.
9/16
B.
4/15
C.
11/15
D.
5/11
E.
None of these

Detailed Solution for Probability - MCQ 3 - Question 18

This will be = 1- prob.(both are same in color)
Prob. of both same in color = [³C₂ + ⁴C₂ + ³C₂]/ ¹⁰C₂ = 12/45
So required prob. = 1 – 12/45

Probability - MCQ 3 - Question 19

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There are 4 black balls and 6 white balls. 2 balls are drawn one by one without replacement. What is the probability that the balls are same in color?

A.
9/21
B.
8/17
C.
5/14
D.
7/15
E.
9/19

Detailed Solution for Probability - MCQ 3 - Question 19

When both black, prob. = 4/10 * 3/9
When both white, prob. = 6/10 * 5/9 Add both cases.

Probability - MCQ 3 - Question 20

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A bag contains 5 red balls and 4 green balls. What is the probability that both balls are same in color?

A.
5/11
B.
4/9
C.
3/13
D.
6/17
E.
None of these

Detailed Solution for Probability - MCQ 3 - Question 20

Case 1: both red
⁵C₂ / ⁹C₂
Case 2: both green
⁴C₂ / ⁹C₂
Add both cases

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