Probability and Statistics - Online Test
Q1. Least square lines of regression give best possible estimates , when ρ(X,Y) is equal to
Answer : Option D
Explaination / Solution:
Least square lines of regression give best possible estimates when the lines coincide at that point ρ=±1
Q2. In how many ways can the word ENGINEER be arranged so that ‘G’ and ‘R’ are never together?
Answer : Option C
Explaination / Solution:
Number of ways of rearranging the word ENGINEER = (8!)/(3!*2!) = 3360
Finding the number of ways of arranging the word ENGINEER such that G and R are always together is done by taking GR as a single alphabet and then finding the permutation.
Number of ways of arranging the word ENGINEER such that G and R are always together = (7!)/(3!*2!) = 420*2 = 840
∴Number of ways of arranging the word ENGINEER such that G and R are never together = Number of ways of rearranging the word ENGINEER - Number of ways of arranging the word ENGINEER such that G and R are always together
⇒Number of ways of arranging the word ENGINEER such that G and R are never together
= 3360 – 840
= 2520
Q3. A fair coin is tossed a fixed number of times. If the probability of getting 4 heads is equal to the probability of getting 7 heads, then the probability of getting 2 heads is
Answer : Option D
Explaination / Solution:
No Explaination.
Q4. ρ(X,Y) is equal to
Answer : Option D
Explaination / Solution:
=
Q5. Read the following information to answer the following questions :
Two unbiased dice are thrown simultaneously
What is the probability of getting a doublet?
Two unbiased dice are thrown simultaneously
What is the probability of getting a doublet?
Answer : Option B
Explaination / Solution:
Total possible outcomes = 6 × 6 = 36
E = Events of getting a doublet
= (1,1), (2,2), (3,3), (4,4), (5,5), (6,6) = 6
PE = 6/36 = 1/6
Q6. From a pack of 52 cards, the cards are drawn one by one till an ace appears. The chance that an ace does not come up in first 26 cards is
Answer : Option A
Explaination / Solution:
No Explaination.
Q7. Quartile deviation is nearly equal to
Answer : Option A
Explaination / Solution:
Quartile deviation is approximately 2/3 times the standard deviation.
Q8.
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
Answer : Option D
Explaination / Solution:
Number of Ways when if at least 3 trainees include in committee =
3C3*10C2 = 1*45 --> 45
Q9. Three of the 6 vertices of a regular hexagon are chosen at random .The probability that the triangle with these vertices is equilateral is
Answer : Option A
Explaination / Solution:
No Explaination.
Q10. For a symmetrical distribution and . The median of the data is
Answer : Option D
Explaination / Solution:
For symmetric distribution,
