# Probability and Statistics (Test 5)

## Cat Entrance Exams : Mathematics Or Quantitative Aptitude

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Q.1
Direction: Study the given information carefully and answer the questions that follow:

A basket contains 5 red, 4 blue, 3 green stones.
If four balls are picked at random, what is the probability that two are blue, one is green and one is red?
A. 2/11
B. 4/13
C. 3/11
D. 3/13
E. None of these
Explaination / Solution:

Probabilities if two are blue and one is green and one is red
= [(4C2*3C1*5C1)/ 12C4] = (6*3*5)/(495) = 2/11

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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 5 men and 5 women be included in a committee

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

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

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Q.3
Directions: In the following questions two equations numbered I and II are given. You have to solve both the equations.
I. 4x2 - 24x + 32 = 0
II. y2 = (12)2 – 140
A. X>Y
B. X ≥Y
C. X
D. X≤Y
E. X = Y or the relationship cannot be established
Explaination / Solution:

I. 4x2 - 24x + 32 = 0
x = (4, 2)
II. y = (+2,-2)
So X ≥Y

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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 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
Explaination / Solution:

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

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Q.5
Direction: Study the given information carefully and answer the questions that follow—
A store contains 3 red, 4 blue, 4 green and 4 whites’ bats.
If two bats are picked at random, what is the probability that both are white?
A. 1/3
B. 3/35
C. 3/5
D. 2/35
E. None of these
Explaination / Solution:

Probabilities if both are White
4C2/15C2 = 6/105 → 2/35

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Q.6
An instructor has a question bank consisting of 300 easy True / False questions,200 difficult True / False questions, 500 easy multiple choice questions and 400 difficult multiple choice questions. If a question is selected at random from the question bank, what is the probability that it will be an easy question given that it is a multiple choice question?
A. 1/9
B. 7/9
C. 4/9
D. 5/9
Explaination / Solution:

 True/False MCQ Easy 300 500 Difficult 200 400

Total = 1400, therefore n(S) = 1400 Let A = event of getting easy question B = event of getting multiple choice question. Workspace
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Q.7
The conditional probability of an event E, given the occurrence of the event F is given by
A. P(E|F)=P(EF)P(F),P(F)<0
B. P(E|F)=P(EF)P(F),P(F)0
C. P(  |   F)   =P(EF)P(F), P(F)0
D. P(E|F)=P(EF)P(E),P(F)0
Explaination / Solution:

The conditional probability of an event E, given the occurrence of the event F is given by :

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Q.8
If P (A) = 0.8, P (B) = 0.5 and P(B|A) = 0.4, find P(A|B)
A. 0.68
B. 0.64
C. 0.66
D. 0.62
Explaination / Solution:

We have ,
P (A) = 0.8, P (B) = 0.5 and P(B|A) = 0.4 Workspace
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Q.9
A dice is tossed once and even number has come up. The chance that it is either 2 or 4 is
A. 2/ 6
B. None of these
C. 4/ 9
D. 2/ 3
Explaination / Solution:

Total number of ways of getting even number is 3

Out of these 3 even number we have to get either 2 or 4 which can be done in 2 ways.

So required probability is 2/3

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Q.10
The letters of the word ‘ ORIENTAL ‘ are arranged in all possible ways . The chance that the consonants and vowels occur alternately is
A. 2/ 35
B. None of these
C. 1/35
D. 1/70