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 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
Q2. A dice is rolled 6 times. The probability of obtaining 2 and 4 exactly three times each is
Answer : Option D
Explaination / Solution:
Total ways of getting 2 and 4 exactly 3 times is 6! / (3! 3!) = 20
Total number of ways in throwing 6 dice is 66
Therefore probability is 20/ 66 = 5/11664
Q3. If the two lines of regression are at right angles , then ρ(X,Y) is equal to
Answer : Option C
Explaination / Solution:
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 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
Q5. A dice has 3 faces each bearing ‘ 2 ‘ and three faces each bearing ‘ 6 ‘. It is rolled once. The probability of showing up ‘a six ‘ is
Answer : Option D
Explaination / Solution:
Total no. of outcomes = 6={2,2,2,6,6,6}
p(getting a six)=3/6=1/2
Q6. If COV(X,Y) = 0 , then the two lines of the regression are
Answer : Option D
Explaination / Solution:
Using the formulae,
here
therefore
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*15+1*20 = 125
Q8. The total area under the standard normal curve is
Answer : Option D
Explaination / Solution:
No Explaination.
Q9. If the variance of the data is V, then its S.D. is
Answer : Option D
Explaination / Solution:
standard deviation have the same units as the data but variance is mean of the square of differences.
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
