Probability and Statistics - Online Test
Q1. 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.
Answer : Option A
Explaination / Solution:
Q2.
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?
Answer : Option D
Explaination / Solution:
Probabilities if both either are Red or either are blue
= (5C2 + 4C2)/12C2 = (10+6)/66 → 8/33
Q3. The two lines of regression are x + 4y = 3 and 3x +y = 15 . value of x for y = 3 is
Answer : Option D
Explaination / Solution:
we have x + 4y = 3 and 3x + y = 15 as the lines of regression of y on x and x on y respectively.
therfore, for y = 3 the required line is x on y
so put y= 3 in 3x + y = 15
we get, x = 4
Q4. An instructor has a question bank consisting of 300 easy True / False questions,200 difficult True / False questions, 500 easy multiple choice questions and 400 difficult multiple choice questions. If a question is selected at random from the question bank, what is the probability that it will be an easy question given that it is a multiple choice question?
Answer : Option E
Explaination / Solution:
| True/False | MCQ |
Easy | 300 | 500
|
Difficult | 200 | 400 |
Total = 1400, therefore n(S) = 1400 Let A = event of getting easy question B = event of getting multiple choice question.
Q5.
Direction: Study the given information carefully and answer the questions that follow:
A basket contains 5 red, 4 blue, 3 green stones.
If four balls are picked at random, what is the probability that two are blue, one is green and one is red?
Answer : Option A
Explaination / Solution:
Probabilities if two are blue and one is green and one is red
= [(4C2*3C1*5C1)/ 12C4] = (6*3*5)/(495) = 2/11
Q6. The mean of 5 observations is 4.4. If three observations are 1,2 and 6 and the difference of the other two is 5, then the other two observations are:
Answer : Option B
Explaination / Solution:
Let other two numbers be x and y
Mean (x) = 4.4 =
this gives ......(1)
Also, ........(2)
Therefore from (1) and (2)
x = 9 and y = 4
Q7. Consider the experiment of throwing a die, if a multiple of 3 comes up, throw the die again and if any other number comes, toss a coin. Find the conditional probability of the event ‘the coin shows a tail’, given that ‘at least one die shows a 3’.
Answer : Option C
Explaination / Solution:
S = {(3,1), (3,2), (3,3), (3,4), (3,5), (3,6), (6,1), (6,2), (6,3), (6,4), (6,5), (6,6), (1,H), (2,H), (4,H), (5,H), (1,T), (2,T), (4,T), (5,T)} Let A = event that coin shows a tail. i.e. A = { (1,T), (2,T), (4,T), (5,T)} and B = event that atleast one die shows 3. B = {(3,1), (3,2), (3,3), (3,4), (3,5), (3,6),(6,3)}
Q8.
Direction: Study the given information carefully and answer the questions that follow—
A store contains 4 red, 5 blue, 4 green shirts.
If two shirts are picked at random, what is the probability that both are green?
Answer : Option C
Explaination / Solution:
Probabilities if both are green
4C2/13C2 = 6/78 → 1/13
Q9. If x and y are related as y – 4x = 3, then the nature of correlation between x and y is
Answer : Option C
Explaination / Solution:
comparinf the given equation with ax + by + c= 0
a = -4, b =1 and c= -3
so ab < 0
hence,
so a perfect positive correlation.
Q10. If P(A) = , P(B) = 0, then P(A|B) is
Answer : Option D
Explaination / Solution:
We know that :
which is not defined
which is not defined
