Probability and Statistics - Online Test

Q1.

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

Answer : Option B
Explaination / Solution:

Number of ways when women are majority in committee = 6C6*7C4 = 1*35 = 35

Q2. Which one of the following average is most affected of extreme observations ?
Answer : Option D
Explaination / Solution:

As A/M is calculated as the sum of all the observations divided by number of observations, so it is affected by if there is any change in the outliers

Q3.

Let ( be a partition of a sample space and suppose that each of  has nonzero probability. Let A be any event associated with S,then


Answer : Option A
Explaination / Solution:

Let {E1, E2, ...,En) be a partition of a sample space and suppose that each of E1, E2, ..., En has nonzero probability. Let A be any event associated with S,then P(A) = P(E1) P (A|E1) + P (E2) P (A|E2) + ... + P (En) P(A|En) .by addition law of probability.

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 at least 5 men to have to be included in a committee

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

Q5. The H.M. of 4,8,16 is
Answer : Option B
Explaination / Solution:

H.M=31a+1b+1c=314+18+116=48/7=6.85
Q6. If P(A) =, P(B) = and P(A ∪ B) = find P(A∩B)
Answer : Option A
Explaination / Solution:



Q7.

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

Answer : Option D
Explaination / Solution:

Number of ways when men are majority in committee = 7C6*6C4+7C7*6C3

7*35+1*20 = 125

Q8. The Mode of the following items is 0,1,6,7,2,3,7,6,6,2,6,0,5,6,0.
Answer : Option B
Explaination / Solution:

6 is the most frequent value here.

Q9. Two events A and B will be independent, if
Answer : Option D
Explaination / Solution:

Two events A and B will be independent, then 


Q10.

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

Answer : Option A
Explaination / Solution:

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