Probability and Statistics | Mathematics or Quantitative Aptitude

# CAT Entrance Exams # Mathematics or Quantitative Aptitude # Probability and Statistics # CBSE 11th Mathematics Prepare / Learn

Q1. The statistical method which helps us to estimate or predict the unknown value of one variable from the known value of the related variable is called

A. scatter diagram

B. regression

C. correlation

D. dispersion

Answer : Option B
Explaination / Solution:

It follows from the definition of regression

# CAT Entrance Exams # Mathematics or Quantitative Aptitude # Probability and Statistics # CBSE 12th Mathematics Prepare / Learn

Q2. If P(A) =

\frac{3}{5}

and P(B) =

\frac{1}{5}

, find P (A ∩ B) if A and B are independent events.

A. 4/25

B. 3/25

C. 7/25

D. 8/25

Answer : Option B
Explaination / Solution:

Since A and B are independent events .
Therefore ,

P (A \cap B) = P (A) . P (B) = \frac{3}{5} \times \frac{1}{5} = \frac{3}{25}

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Q3. The conditional probability of an event E, given the occurrence of the event F is given by

A. P(E|F)=P(E∩F)P(F),P(F)<0

B. P(E|F)=P(E∪F)P(F),P(F)≠0

C. P(E | F) =P(E∩F)P(F), P(F)≠0

D. P(E|F)=P(E∩F)P(E),P(F)≠0

Answer : Option C
Explaination / Solution:

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

P (E | F) = \frac{P (E \cap^{} F)}{P (F)}, P (F) \neq 0

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Q4.

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

# CAT Entrance Exams # Mathematics or Quantitative Aptitude # Probability and Statistics # CBSE 11th Mathematics Prepare / Learn

Q5. The coefficient of correlation r satisfies

A. − 1 < r < 0

B. I r I > 1

C. 0 < r < 1

D. I r I ≤ 1

Answer : Option D
Explaination / Solution:

r can't be numerically more than 1

# CAT Entrance Exams # Mathematics or Quantitative Aptitude # Probability and Statistics # CBSE 12th Mathematics Prepare / Learn

Q6. The conditional probability of an event E, given the occurrence of the event F lies between

A. 0 < P (E|F) ≤ 1

B. 0 < P (E|F) < 1

C. 0 ≤ P (E|F) ≤ 1

D. 0 ≤ P (E|F) < 1

Answer : Option C
Explaination / Solution:

As the probability of any event always lies between 0 and 1. Therefore , 0 ≤ P (E|F) ≤ 1.

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Q7.

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

# CAT Entrance Exams # Mathematics or Quantitative Aptitude # Probability and Statistics # CBSE 11th Mathematics Prepare / Learn

Q8. S.D. of a data is 6. When each observation is increased by 1, then the S.D. of new data is

A. 7

B. 8

C. 5

D. 6

Answer : Option D
Explaination / Solution:

$S . D = \sqrt{\frac{n^{2} - 1}{12}}$

so it depends only on number of observations not on individual observations.

# CAT Entrance Exams # Mathematics or Quantitative Aptitude # Probability and Statistics # CBSE 12th Mathematics Prepare / Learn

Q9. The conditional probability of the event E', given that F has occurred is given by

A. P (E′|F) = 1

B. P (E′|F) = P (E|F)

C. P (E′|F) = 1 – P (E|F)

D. P (E′|F) = – 1 + P (E|F)

Answer : Option C
Explaination / Solution:

we know that P(S/F) =1

$⟹$ P(E U E'|F)=1 since EUE' =S

$⟹$ P(E/F) +P(E'/F) =1 since E and E' are disjoint events

P(E'/F) = 1- P(E/F)

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Q10.

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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