CBSE 12TH MATHEMATICS - Online Test
Q1. A laboratory blood test is 99% effective in detecting a certain disease when it is in fact, present. However, the test also yields a false positive result for 0.5% of the healthy person tested (i.e. if a healthy person is tested, then, with probability 0.005, the test will imply he has the disease). If 0.1 percent of the population actually has the disease, what is the probability that a person has the disease given that his test result is positive?
Answer : Option A
Explaination / Solution:
Let
are events that a person has disease and the person has not disease. .
Let A = event that the test result is positive.
are events that a person has disease and the person has not disease. .
Let A = event that the test result is positive.
Q2. A random variable is a real valued function whose domain is the.
Answer : Option B
Explaination / Solution:
A random variable is a real valued function whose domain is the sample space of a random experiment .
Q3. Let X be a random variable assuming values x1, x2,....,xn with probabilities p1, p2, ...,pn, respectively such that pi ≥ 0,. Mean of X denoted by is defined as
Answer : Option B
Explaination / Solution:
Let X be a random variable assuming values x1, x2,....,xn with probabilities p1, p2, ...,pn, respectively such that pi ≥ 0,. Mean of X denoted by is defined as: .
Q4. An urn contains 5 red and 2 black balls. Two balls are randomly drawn. Let X represent the number of black balls. What are the possible values of X? Is X a random variable ?
Answer : Option C
Explaination / Solution:
An urn contains 5 red and 2 black balls. Two balls are randomly drawn. Let X represent the number of black balls.therefore the possible values of X = 0 , 1 ,2 . Yes , X is a random variable.
Q5. Let X represent the difference between the number of heads and the number of tails obtained when a coin is tossed 6 times. What are possible values of X?
Answer : Option A
Explaination / Solution:
Let X represent the difference between the number of heads and the number of tails obtained when a coin is tossed 6 times. When a coin is tossed 6 times , we have 64 outcomes which consists of : (i) 6 heads and 0 tails (ii) 5 heads and 1 tail (iii) 4 heads and 2 tails (iv) 3 heads and 3 tails (v) 2 heads and 4 tails (vi) 1 head and 5 tails (vii) 0 head and 6 tails . Let X represents the difference between the number of heads and tails. (i) X = 6 – 0 = 6 (ii) X = 5 – 1 = 4 (iii) X = 4 – 2 = 2 (iv) X = 3 – 3 = 0 (v) X = 4 – 2 = 2 (vi) X = 5 – 1 = 4 (vii) X = 6 – 0 = 6 . Therefore , X = 6 , 4 , 2, 0 .
Q6. Find the mean number of heads in three tosses of a fair coin.
Answer : Option C
Explaination / Solution:
Let X is the random variable of “number of heads “ X = 0, 1, 2, 3.
Therefore, the probability distribution is:
Therefore, the probability distribution is:
Q7. Two dice are thrown simultaneously. If X denotes the number of sixes, find the expectation of X.
Answer : Option B
Explaination / Solution:
Let A = event of getting 6 on the dice .
A = {(6,1),(6,2),(6,3),(6,4),(6,5),(6,6),(1,6),(2,6),(3,6),(4,6),(5,6)}
Let X is the random variable of “ number of sixes “.
Therefore, X = 0 , 1, ,2 .
A = {(6,1),(6,2),(6,3),(6,4),(6,5),(6,6),(1,6),(2,6),(3,6),(4,6),(5,6)}
Let X is the random variable of “ number of sixes “.
Therefore, X = 0 , 1, ,2 .
Q8. Two numbers are selected at random (without replacement) from the first six positive integers. Let X denote the larger of the two numbers obtained. Find E(X).
Answer : Option B
Explaination / Solution:
First 6 positive integers are 1,2,3,4,5,6. As 1 is the smallest positive integer. Therefore , X = 2,3,4,5,6.
Q9. In a meeting, 70% of the members favour and 30% oppose a certain proposal.A member is selected at random and we take X = 0 if he opposed, and X = 1 if he is in favour. Find E(X) and Var (X).
Answer : Option C
Explaination / Solution:
Here X = 0, 1.
Therefore, the probability distribution is:
Therefore, the probability distribution is:
