JEE-Main - Grade 12 - Mathematics - Probability - Introduction and Snapshot of Probability - Study ref# 935

Introduction
In earlier Classes, we have studied the
probability as a measure of uncertainty of events in a random experiment. We discussed
the axiomatic approach formulated by Russian Mathematician, A.N. Kolmogorov
(1903 - 1987) and trea... read more

JEE-Main - Grade 12 - Mathematics - Probability - Introduction and Snapshot of Probability - Study ref# 936

Following sections must be covered to
understand the Probability:
1. Conditional Probability.
2. Multiplication Theorem on Probability.
3. Independent Events
4. Bayes’ Theorem
5. Random Variables and its Probability
Distributi... read more

JEE-Main - Grade 12 - Mathematics - Probability - Target Setup for Probability - Study ref# 937

Student requires to achieve the following milestones to get better grip over Probability. The milestones / targets are as follows: Starting Point: Days 0Test TypeAppear on TestTarget TestsScorePractice Test000%Chapter Test000%Sub... read more

JEE-Main - Grade 11 - Mathematics - Sets - Importance and Snapshot of Sets - Study ref# 602

Introduction:
The concept of set is the fundamental part of Mathematics.
The study of geometry, probability, trigonometry etc. needs the knowledge of
set.
The theory of set was first developed by German
mathematician Georg Cantor. H... read more

JEE-Main - Grade 11 - Mathematics - Probability - Importance and Snapshot of Probability - Study ref# 647

Introduction
In earlier classes, we have studied about the concept of
probability as a measure of uncertainty of various phenomenon. In general, to
obtain the probability of an event, we find the ratio of the number of
outcomes favorable ... read more

JEE-Main - Grade 11 - Mathematics - Probability - Importance and Snapshot of Probability - Study ref# 648

Following sections must be covered to understand
Probability:
1. Random Experiment
2. Event
3. Axiomatic Approach to Probability... read more

JEE-Main - Grade 11 - Mathematics - Probability - Target Setup for Probability - Study ref# 649

Student requires to achieve the following milestones to get better grip over Probability. The milestones / targets are as follows:-Starting Point: Days 0Test TypeAppear on TestTarget TestsScorePractice Test000%Chapter Test000%Subject ... read more

JEE-Main - Grade 11 - Chemistry - Structure of Atom - Study ref# 1218

Why was a change in the Bohr model of atom required, due
to which important development(s), concept of movement of an electron in an
orbit was replaced by the concept of probability of finding electron in an
orbital? What is the name given t... read more

JEE-Main - Grade 11 - Mathematics - Probability - Study ref# 2901

A coin is tossed three times. Answer: We know that sample space means a set of all possible
events occurring in an experiment. If a coin is tossed three times ,then
possible outcomes are
{HHH,HHT,HTT,THH,THT,HTH,TTH,TTT}
where, H repre... read more

JEE-Main - Grade 11 - Mathematics - Probability - Study ref# 2902

A coin is tossed four times. Answer: The sample space
S={HHHH,HHHT,HHTH,HHTT,HTHH,HTHT,HTTH,HTTT,THHH,THHT,THTH,THTT,TTHH,TTHT,TTTH,TTTT}
where, H and T represent head and tail of a coin. ... read more

JEE-Main - Grade 11 - Mathematics - Probability - Study ref# 2903

A coin is tossed and then a die is rolled only in a case a
head is shown on the coin. Answer: The sample space S is S={H1,H2,H3,H4,H5,H6}
where ,H represent a head of a coin. ... read more

JEE-Main - Grade 11 - Mathematics - Probability - Study ref# 2904

2 boys and 2 girls are in room X and 1 boy and 3 girls in
room Y. Specify the sample space for the experiment in which a room is
selected and then
a person. Answer: X
and
If then
show that lies in the interval. Answer: We know that,
... read more

JEE-Main - Grade 11 - Mathematics - Probability - Study ref# 3191

If A and B are two independent events, prove that where C is an event
defined that exactly one of A and B occurs. Answer: Here,
[Since A ,B are independent, so A’,B’ are independent]
... read more

JEE-Main - Grade 11 - Mathematics - Probability - Study ref# 3192

A is targeting to B, B and C are targeting to A.
Probability to hitting the target by A, B and C are and , respectively. If A is
hit, then find the probability that B hits the target and C do... read more

JEE-Main - Grade 11 - Mathematics - Probability - Study ref# 3193

A box contains N coins, m is which are fair and the rest
are biased. The probability of getting a heard when a fair coin is tossed, is
1/2 , while it 2/3 when a biased coin is tossed. A coin is drawn from the box
at random and is tossed twic... read more

JEE-Main - Grade 12 - Mathematics - Probability - Study ref# 9648

If and
, find
(i)
(ii)
(iii) read more

JEE-Main - Grade 12 - Mathematics - Probability - Study ref# 9649

Evaluate if
First use formula and find by using the formula, Answer: Given,
Now... read more

JEE-Main - Grade 12 - Mathematics - Probability - Study ref# 9650

A coin is tossed three times
(i) E: head on third toss F: head on
first two tosses
(ii) E: almost two heads F: almost two
heads
(iii) E: almost two tails F: almost two
tails Answer: When a coin is tossed three time... read more

JEE-Main - Grade 12 - Mathematics - Probability - Study ref# 9651

Mother, father and son line up at random
for a family picture
E: son on
one end
F: father
in middle Answer: If mother (m), father (f)
and son (s) line up for the family picture, then the sample space will
be S = {mfs, msf, ... read more

JEE-Main - Grade 12 - Mathematics - Probability - Study ref# 9652

A fair die is rolled. Consider events and .Find
(i) and
(ii) and
(iii) ... read more

JEE-Main - Grade 12 - Mathematics - Probability - Study ref# 9653

An instructor has a question bank
consisting of 300 easy true/false questions, 200 difficult true/false, 500
easy multiple choice questions and 400 difficult multiple choice questions.
If a question is selected at random from the test bank, ... read more

JEE-Main - Grade 12 - Mathematics - Probability - Study ref# 9654

If , then is
(a) Zero
(b)
(c) not defined
(d) 1 Answer: It is given that ... read more

JEE-Main - Grade 12 - Mathematics - Probability - Study ref# 9655

If A and B are events such
that then
(a)
(b)
(c)
(d) read more

JEE-Main - Grade 12 - Mathematics - Probability - Study ref# 9656

Two cards are drawn at random and without
replacement from a pack of 52 playing cards. Find the probability that both
the cards are black. Answer: There are 26 black cards in a pack of 52
cards.
Required Probability = P(E and F) =
P(E)... read more

JEE-Main - Grade 12 - Mathematics - Probability - Study ref# 9657

A die marked 1, 2, 3 in red and 4, 5, 6
in green is tossed. Let A be the event, ‘number is even’ and B be the event,
‘number is red’. Are A and B independent? Answer: When a die is thrown, the sample space S
= {1, 2, 3, 4, 5, 6}.
Also, A#... read more

JEE-Main - Grade 12 - Mathematics - Probability - Study ref# 9658

Let E and F be events with. Are E and F independent? Answer: It is given that
Now,
Therefore, E and F are not independent
events.... read more

JEE-Main - Grade 12 - Mathematics - Probability - Study ref# 9659

Events A and B are such that State whether A and
B are independent? Answer: Given, read more

JEE-Main - Grade 12 - Mathematics - Probability - Study ref# 9660

A die is tossed thrice. Find the
probability of getting an odd number atleast once.
Note: The probability of getting an odd
number atleast once
= 1- probability of getting an odd number
in none of the throws. Answer: When a die is ... read more

JEE-Main - Grade 12 - Mathematics - Probability - Study ref# 9661

In a hostel, 60% of the students read
Hindi newspaper, 40% read English newspaper and 20% read both Hindi and
English newspapers. A student is selected at random,
(i) Find the probability that he/she
reads neither Hindi nor English newspa... read more

JEE-Main - Grade 12 - Mathematics - Probability - Study ref# 9662

An urn contains 5 red and 5 black balls.
A ball is drawn at random, its colour is noted and is returned to the urn.
Moreover, 2 additional balls of the colour drawn are put in the urn and then
a balls is drawn at random. What is the probabil... read more

JEE-Main - Grade 12 - Mathematics - Probability - Study ref# 9663

A bag contains 4 red and 4 black balls,
another bag contains 2 red and 6 black balls. Once of the two bag is selected
at random and a ball is drawn from the bag which is found to be red. Find the
probability that the ball is drawn from the f... read more

JEE-Main - Grade 12 - Mathematics - Probability - Study ref# 9664

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 p... read more

JEE-Main - Grade 12 - Mathematics - Probability - Study ref# 9665

A manufacturer has three machine
operators A, B and C. The first operator A produces 1% defective items,
whereas the other two operators B and C produce 5% and 7 % defective items,
respectively. A is on the job for 50% of the time, B on the ... read more

JEE-Main - Grade 12 - Mathematics - Probability - Study ref# 9666

An urn contains 5 red and 2 black balls.
Two balls are randomly selected. Let X represent the number of black balls.
What are the possible values of X? Is X a random variable? Answer: The two balls are selected can be
represented as BB, BR, ... read more

JEE-Main - Grade 12 - Mathematics - Probability - Study ref# 9667

Find the probability distribution of the
number of successes in two tosses of a die, where a success is defined as
(i) number greater than 4
(ii) six appears on the die. Answer: When a die is tossed two times, we obtain
(6 × 6) = 36 n... read more

JEE-Main - Grade 12 - Mathematics - Probability - Study ref# 9668

A pair of dice is thrown 4 times. If
getting a doublet is considered a success, find the probability of two
successes. Answer: It is a case of Bernoulli trials with n =
4. Here, success is getting a doublet.
When a pair of dice is thrown ... read more

JEE-Main - Grade 12 - Mathematics - Probability - Study ref# 9669

Five cards are drawn successively with
replacement from a well- shuffled deek of 52 cards. What is the probability
that
(i) all the five cards are spades?
(ii) only 3 cards are spades?
(iii) none is a spade? Answer: Let X represent the... read more

JEE-Main - Grade 12 - Mathematics - Probability - Study ref# 9670

The probability that a student is not a
swimmer is 1/5. The probability that out of five students, four are swimmers
is
(i)
(ii)
... read more

JEE-Main - Grade 12 - Mathematics - Probability - Study ref# 9671

In a hurdle race, a player has to cross
10 hurdles. The probability that he will clear each hurdles is what is the probability
that he will knock down fewer than 2 hurdles? Answer: It is a case of Bernoulli trials, where
success is crossing... read more

JEE-Main - Grade 12 - Mathematics - Probability - Study ref# 9672

If a leap year is selected at random,
what is the chance that it will contain 53 Tuesday?
Note: In a leap year, there are 366 days
having 52 weeks and 2 extra days. Answer: In a leap year, there are 366 days i.e.,
52 weeks and 2 days.
... read more

JEE-Main - Grade 12 - Chemistry - Chemical Kinetics - Study ref# 9751

Activation energy of a chemical reaction
can be determined by…….. .
(a) determining the rate constant at
standard temperature
(b) determining the rate constant at two
temperatures
(c) determining probability of collision
... read more