# Probability and Statistics (Test 4)

## 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 two balls are picked at random, what is the probability that either both are red or both are blue?
A. 7/95
B. 4/55
C. 5/33
D. 8/33
E. None of these
Explaination / Solution:

Probabilities if both either are Red or either are blue
= (5C2 + 4C2)/12C2 = (10+6)/66 → 8/33

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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 6 men and 4 women be included in a committee

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

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

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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. 8x – y = 40
II. 4x + y = 32
A. X>Y
B. X ≥Y
C. X
D. X≤Y
E. X = Y or the relationship cannot be established
Explaination / Solution:

After solving the both equation got values of x = 6 and y = 8 So X
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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 6 men and 4 women be included in a committee
A. 105
B. 114
C. 81
D. 210
E. None of these
Explaination / Solution:

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

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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 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
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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Q.6
A black and a red dice are rolled. Find the conditional probability of obtaining the sum 8, given that the red die resulted in a number less than 4.
A. 1/9
B. 4/9
C. 5/9
D. 7/9
Explaination / Solution: Workspace
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Q.7
If P(A) =  and P(B) = , find P (A ∩ B) if A and B are independent events.
A. 4/25
B. 3/25
C. 7/25
D. 8/25
Explaination / Solution:

Since A and B are independent events .
Therefore ,

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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. 0.32
B. 0.29
C. 0.35
D. 0.37
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
Neelam and Nidhi throw with a dice .The chance that both Neelam and Nidhi throw the same number is
A. 1/ 6
B. none of these
C. 1/ 36
D. 1/ 2
Explaination / Solution:

TOTAL NO. OF OUTCOMES=62=36

no. of outcomes in which both throws same no.={(1,1),(2,2),(3,3),(4,4),(5,5),(6,6)}=6

p(both throws same no.)=6/36=1/6

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Q.10
The letters of the word ‘ MALENKOV ‘are arranged in all possible ways. The chance that there are exactly four letters between M and E is
A. 3/ 14
B. 1/ 14
C. None of these
D. 3/28