Probability and Statistics (Test 3)

Problem Solving And Reasoning : Mathematics Or Quantitative Aptitude

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Probability and Statistics

Probability and Statistics
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Q.1
Directions: Study the given information carefully and answer the questions that follow— 
A store contains 5 red, 4 blue, 5 green shirts.
If two shirts are picked at random, what is the probability that at most one is blue?
A. 15/91
B. 85/91
C. 25/29
D. 75/91
E. None of these
Answer : Option B
Explaination / Solution:

Probabilities if at most one is blue = 
[(4C0*10C24C1*10C1)/14C2] = (1*45 + 4*10)/( 91) = 85/91

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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 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.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 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.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*15+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
In a basket there are 7 apples and 8 oranges. 4 fruits are picked at random. What is the probability that two fruits are apples and 2 are oranges?
A. 72/455
B. 82/455
C. 89/455
D. 84/455
E. None of these
Answer : Option E
Explaination / Solution:

Total number of fruits n(s) =7 + 8=15 
Probability  = (7C2*8C2)/15C4
= (21*28)/1365 = 28/65

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Q.8
In how many ways the letter of the word IMMEDIATELY can be arranged so that vowels always come together ?
A. 56800
B. 75600
C. 64800
D. 84560
E. None of these
Answer : Option C
Explaination / Solution:

There are 11 letters .out of which 5 are vowels and 6 are consonants. 
So taking vowels together as a single letter , we have 7 letters 
So no of arrangements =( 7! * 5!)/ (2!)3 [there are 2 i,m e]

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Q.9
In how many ways can the word ENGINEER be arranged so that ‘G’ and ‘R’ are never together?
A. 3120
B. 2830
C. 2520
D. 3220
E. None of these
Answer : Option C
Explaination / Solution:

Number of ways of rearranging the word ENGINEER  = (8!)/(3!*2!) = 3360 
Finding the number of ways of arranging the word ENGINEER such that G and R are always together is done by taking GR as a single alphabet and then finding the permutation. 
Number of ways of arranging the word ENGINEER such that G and R are always together = (7!)/(3!*2!) = 420*2 = 840
∴Number of ways of arranging the word ENGINEER such that G and R are never together = Number of ways of rearranging the word ENGINEER - Number of ways of arranging the word ENGINEER such that G and R are always together 
⇒Number of ways of arranging the word ENGINEER such that G and R are never together 
= 3360 – 840 
= 2520

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Q.10
Read the following information to answer the following questions : 
Two unbiased dice are thrown simultaneously

What is the probability of getting a doublet?
A. 1/3
B. 1/6
C. 1/4
D. 2/3
E. None of these
Answer : Option B
Explaination / Solution:

Total possible outcomes = 6 × 6 = 36 
E = Events of getting a doublet 
= (1,1), (2,2), (3,3), (4,4), (5,5), (6,6) = 6 
PE = 6/36 = 1/6

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