Probability Test-04

This is Probability Test-04 for CBSE class 12 Maths.. There are 15 questions in this test with each question having around four answer choices.

Questions & Answers

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?

A
\(\frac{{25}}{{133}}\;\)
B
\(\frac{{27}}{{133}}\)
C
\(\frac{{22}}{{133}}\)
Correct
D
\(\frac{{23}}{{133}}\)

There are three coins. One is a two headed coin (having head on both faces),another is a biased coin that comes up heads 75% of the time and third is an unbiased coin. One of the three coins is chosen at random and tossed, it shows heads, what is the probability that it was the two headed coin ?

A
\({\text{\;}}\frac{5}{9}\)
B
\(\frac{2}{{9\;}}\)
C
\(\frac{4}{9}\)
Correct
D
\(\frac{1}{9}\)

An insurance company insured 2000 scooter drivers, 4000 car drivers and 6000 truck drivers. The probability of an accidents are 0.01, 0.03 and 0.15 respectively. One of the insured persons meets with an accident. What is the probability that he is a scooter driver?

A
\(\frac{5}{{52}}\)
B
\(\frac{1}{4}\)
C
\(\frac{1}{{52}}\)
Correct
D
\(\frac{3}{{52}}\)

A random variable is a real valued function whose domain is the.

A
set of real numbers
B
sample space of a random experiment
Correct
C
set of irrational numbers
D
set of integers

Let X be a random variable assuming values x1, x2,....,xn with probabilities p1, p2, ...,pn, respectively such that pi ≥ 0,\(\mathop \sum \limits_{i = 1}^n {p_i} = 1\). Mean of X denoted by \(\mu \) is defined as

A
\(\mu = \;\mathop \sum \limits_{i - 1}^n {x_i}{p_{i + 1}}\)
B
\(\mu = \;\mathop \sum \limits_{i - 1}^n {x_i}{p_i}\)
Correct
C
\(\mu = \;\mathop \sum \limits_{i - 1}^n {x_i}\)
D
\(\mu = \;\mathop \sum \limits_{i - 1}^n {p_i}\)

Let X be a random variable assuming values x1, x2,....,xn with probabilities p1, p2, ...,pn, respectively such that pi ≥ 0,\(\mathop \sum \limits_{i = 1}^n {p_i} = 1\). If E is the expectation, mean of X is denoted by \(\mu \), variance denoted by σ2, is defined as

A
σ2=E(X – \(\mu \))3
B
σ2=E(X + \(\mu \))2
C
σ2=E(X – \(\mu \))
D
σ2=E(X – \(\mu \))2
Correct

A random variable X taking values 0, 1, 2, ..., n is said to have a binomial distribution with parameters n and p, if its probability distribution is given by

A
\(P\left( {X = r} \right) = C_r^n{p^r}{q^{n - r - 2}}\)
B
\(P\left( {X = r} \right) = C_{r - 2}^n{p^r}{q^{n - r}}\)
C
\(P\left( {X = r} \right) = C_r^n{p^{2r}}{q^{n - r}}\)
D
\(P\left( {X = r} \right) = C_r^n{p^r}{q^{n - r}}\)
Correct

State which of the following is a probability distribution of a random variable.

A
Z 3 2 1 0 – 1 P(Z) 0.3 0.2 0.4 0.1 0.05
B
Y – 1 0 1 P(Y) 0.6 0.1 0.2
C
X 0 1 2 3 4 P(X) 0.1 0.5 0.2 – 0.1 0.3
D
X 0 1 2 P(X) 0.4 0.4 0.2
Correct

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 ?

A
X = 2, 3, 5; yes
B
X = 2, 1, 3; yes
C
X = 0, 1, 2; yes
Correct
D
X = 2, 3, 4; no

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?

A
X = 6, 5, 2, 0
B
X = 6, 3, 2, 1
C
X = 6, 4, 2, 1
D
X = 6, 4, 2, 0
Correct

Find the mean number of heads in three tosses of a fair coin.

A
1.4
B
1.2
C
1.0
D
1.5
Correct

Two dice are thrown simultaneously. If X denotes the number of sixes, find the expectation of X.

A
\(\frac{1}{4}\)
B
\(\frac{1}{6}\)
C
\(\frac{1}{5}\;\)
D
\(\frac{1}{3}\)
Correct

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).

A
\(\frac{{11}}{3}\)
B
\(\frac{{16}}{3}\)
C
\(\frac{{14}}{3}\)
Correct
D
\(\frac{{10}}{3}\)

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).

A
E(X) = 0.7 and Var (X) = 0.21
Correct
B
E(X) = 0.8 and Var (X) = 0.14
C
E(X) = 0.9 and Var (X) = 0.29
D
E(X) = 0.6 and Var (X) = 0.22

The mean of the numbers obtained on throwing a die having written 1 on three faces, 2 on two faces and 5 on one face is

A
1
B
4
C
2
Correct
D
5