Probability and Statistics

Probability and Statistics

Probability and Statistics
| Probability and Statistics |
Q.1
If two shirts are picked at random, what is the probability that at most one is blue,?
A. 24/25
B. 17/39
C. 34/39
D. 11/13
E. None of these
Answer : Option C
Explaination / Solution:

Probabilities if at most one is blue = 
[(5C0*8C25C1*8C1)/ 13C2] = (1*28 + 5*8)/(78) = 34/39

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Q.2

Direction: Study the following information carefully and answer the questions that follow:

A committee of 10 persons is to be formed from 7 men and 6 women

In how many ways of these committee the women are in majority

A. 45
B. 35
C. 110
D. 56
E. None of these
Answer : Option B
Explaination / Solution:

Number of ways when women are majority in committee = 6C6*7C4 = 1*35 = 35

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Q.3

Direction: Study the following information carefully and answer the questions that follow:

A committee of 10 persons is to be formed from 7 men and 6 women

In how many ways this can be done if at least 5 men to have to be included in a committee

A. 251
B. 265
C. 167
D. 340
E. None of these
Answer : Option A
Explaination / Solution:

Number of Ways when if at least 5 men include in committee = 7C5*6C5+7C6*6C4+7C7*6C3

21*6+7*15+1*20 = 251

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Q.4

Direction: Study the following information carefully and answer the questions that follow:

A committee of 10 persons is to be formed from 7 men and 6 women

In how many of these committee the men are in majority

A. 118
B. 135
C. 140
D. 125
E. None of these
Answer : Option D
Explaination / Solution:

Number of ways when men are majority in committee = 7C6*6C4+7C7*6C3

7*35+1*20 = 125

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Q.5

Direction: Study the following information carefully and answer the questions that follow:

A committee of 10 persons is to be formed from 7 men and 6 women

In how many ways this can be done if 6 men and 4 women be included in a committee

A. 105
B. 114
C. 81
D. 210
E. None of these
Answer : Option A
Explaination / Solution:

If 6 men and 4 women include in committee = 7C6*6C4 --> 7*15 --> 105

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Q.6

Direction: Study the following information carefully and answer the questions that follow:

A committee of 10 persons is to be formed from 7 men and 6 women

In how many ways this can be done if 5 men and 5 women be included in a committee

A. 102
B. 140
C. 136
D. 126
E. None of these
Answer : Option D
Explaination / Solution:

If 5 men and 5 women include in committee = 7C5*6C5 --> 21*6 = 126

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Q.7

Direction: Study the following information carefully and answer the questions that follow:

A committee of five members is to be formed out of 3 trainees, 4 professors and 6 engineers.

In how many ways this can be done if at least 3 trainees to have to be included in a committee

A. 25
B. 95
C. 65
D. 45
E. None of these
Answer : Option D
Explaination / Solution:

Number of Ways when if at least 3 trainees include in committee =

3C3*10C2 = 1*45 --> 45

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Q.8

Direction: Study the following information carefully and answer the questions that follow:

A committee of five members is to be formed out of 3 trainees, 4 professors and 6 engineers.

In how many ways this can be done if 2 trainees and 3 engineer to have to be included in a committee

A. 32
B. 60
C. 45
D. 90
E. None of these
Answer : Option B
Explaination / Solution:

If 2 trainees and 3 engineers include in committee

3C2*6C3 = 3*20 --> 60

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Q.9

Direction: Study the following information carefully and answer the questions that follow:

A committee of five members is to be formed out of 3 trainees, 4 professors and 6 engineers.

In how many ways this can be done if at least 2 trainees to have to be included in a committee

A. 340
B. 820
C. 560
D. 405
E. None of these
Answer : Option D
Explaination / Solution:

If at least 2 trainees include in committee

3C2*10C3 + 3C3*10C2 = 3*120+1*45

= 405

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Q.10

Direction: Study the following information carefully and answer the questions that follow:

A committee of five members is to be formed out of 3 trainees, 4 professors and 6 engineers.

In how many ways this can be done if 3 engineers and 2 professors or 2 trainees and 3 professor be included in a committee

A. 140
B. 160
C. 132
D. 155
E. None of these
Answer : Option C
Explaination / Solution:

If 3 engineers and 2 professors or 2 trainees and 3 professors include in committee

6C3*4C2 + 3C2*4C3 = 20*6 + 3*4 = 120 + 12 = 132

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