# Probability and Statistics (Test 3)

## Cat Entrance Exams : Mathematics Or Quantitative Aptitude

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Probability and Statistics
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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 three balls are picked at random, what is the probability that at least one is green?
A. 11/13
B. 43/53
C. 34/55
D. 13/55
E. None of these
Explaination / Solution:

Probability if at least one is Green
[1-(9C3/12C3)] = 84/220 → 34/55

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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 of these committee the men are in majority

A. 118
B. 135
C. 140
D. 125
E. None of these
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.3
Direction: In the following question, there are two equations. Solve the equations and answer accordingly:
I. 6x2 + 46x +60 = 0
II. 4y2+ 29y + 45= 0
A. X>Y
B. X ≥Y
C. X
D. X≤Y
E. X = Y or the relationship cannot be established
Explaination / Solution:

I. 6x2 + 46x +60 = 0
3x2 + 23x + 30 = 0
3x2 + 18x + 5x + 30 = 0
3x(x+6)+5(x+6)=0
(x+6)(3x+5)=0
x = -5/3, -6

II. 4y2 + 29y + 45= 0
4y2 + 20y + 9y + 45= 0
4y(y+5)+9(y+5)=0
(4y+9)(y+5)=0
y = -5, -9/4

So Relationship cannot be established

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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
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 five members is to be formed out of 3 trainees, 4 professors and 6 engineers.
In how many ways this can be done if 1 trainees and 4 engineers be included in a committee
A. 45
B. 32
C. 60
D. 36
E. None of these
Explaination / Solution:

If 1 trainees and 4 engineers include in committee
3C1*6C4 = 3*15 --> 45

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Q.6
A black and a red dice are rolled. Find the conditional probability of obtaining a sum greater than 9, given that the black die resulted in a 5.
A. 2/3
B. 5/9
C. 1/3
D. 4/9
Explaination / Solution:

n(S)=36.
Let A = event of getting sum greater than 9.
= {(4,6),(5,5),(6,4),(5,6),(6,5),(6,6)}
And B = event of getting 5 on black die.
={(5,1),(5,2),(5,3),(5,4),(5,5),(5,6)}

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Q.7
Two events A and B will be independent, if
A. P(A) = P(B)
B. P(A) + P(B) = 1
C. A and B are mutually exclusive
D. P(A′B′) = [1 – P(A)] [1 – P(B)]
Explaination / Solution:

Two events A and B will be independent, then

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Q.8
Compute P(A|B), if P(B) = 0.5 and P (A ∩ B) = 0.32
A. P(A|B) =
B. P(A|B) =
C. P(A|B) =
D. P(A|B) =
Explaination / Solution:

We have , P(B) = 0.5 and P (A ∩ B) = 0.32

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Q.9
The total area under the standard normal curve is
A. None of these
B. 1
C. 2
D. 1/2
Explaination / Solution:
No Explaination.

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Q.10
Three prizes are distributed among three persons at random. The chances that none of the persons gets all the prizes is
A. 6/ 216
B. 210/ 216
C. 120/ 216
D. none of these