Q. In a survey, 60% of people like tea, 30% like coffee, and 10% like both. What is the probability that a person likes coffee given that they like tea?
Q. In a survey, 60% of people like tea, and 40% like coffee. If a person is chosen at random, what is the probability that they like coffee given that they do not like tea?
A.
0.4
B.
0.6
C.
0.5
D.
1
Solution
If a person does not like tea, they must like coffee. Therefore, the probability is 1.
Q. In a survey, 70% of people like tea and 30% like coffee. If a person is chosen at random, what is the probability that they like tea given that they do not like coffee?
A.
1/3
B.
2/3
C.
1/2
D.
1
Solution
If a person does not like coffee, they must like tea. Therefore, P(Tea | Not Coffee) = 1.
Q. In a survey, 70% of people like tea and 40% like coffee. If 30% like both, what is the probability that a person likes coffee given that they like tea?
Q. In a survey, 70% of people like tea, and 40% like coffee. If 30% like both tea and coffee, what is the probability that a person likes coffee given that they like tea?
A.
0.4
B.
0.3
C.
0.5
D.
0.6
Solution
Using conditional probability, P(Coffee|Tea) = P(Coffee and Tea) / P(Tea) = 0.3 / 0.7 = 3/7.
Q. In a survey, 70% of people like tea, and 40% like coffee. If 30% like both tea and coffee, what is the probability that a person likes tea given that they like coffee?
A.
0.5
B.
0.7
C.
0.3
D.
0.4
Solution
Using conditional probability, P(Tea | Coffee) = P(Tea and Coffee) / P(Coffee) = 0.3 / 0.4 = 0.75.
The Mathematics Syllabus for JEE Main is crucial for students aiming to excel in competitive exams. Understanding this syllabus not only helps in grasping key concepts but also enhances your ability to tackle objective questions effectively. Practicing MCQs and important questions from this syllabus is essential for solid exam preparation, ensuring you are well-equipped to score better in your exams.
What You Will Practise Here
Sets, Relations, and Functions
Complex Numbers and Quadratic Equations
Permutations and Combinations
Binomial Theorem
Sequences and Series
Limits and Derivatives
Statistics and Probability
Exam Relevance
The Mathematics Syllabus (JEE Main) is not only relevant for JEE but also appears in CBSE and State Board examinations. Students can expect a variety of question patterns, including direct MCQs, numerical problems, and conceptual questions. Mastery of this syllabus will prepare you for similar topics in NEET and other competitive exams, making it vital for your overall academic success.
Common Mistakes Students Make
Misinterpreting the questions, especially in word problems.
Overlooking the importance of units and dimensions in problems.
Confusing formulas related to sequences and series.
Neglecting to practice derivations, leading to errors in calculus.
Failing to apply the correct methods for solving probability questions.
FAQs
Question: What are the key topics in the Mathematics Syllabus for JEE Main? Answer: Key topics include Sets, Complex Numbers, Permutations, Binomial Theorem, and Calculus.
Question: How can I improve my performance in Mathematics MCQs? Answer: Regular practice of MCQs and understanding the underlying concepts are essential for improvement.
Now is the time to take charge of your exam preparation! Dive into solving practice MCQs and test your understanding of the Mathematics Syllabus (JEE Main). Your success is just a question away!
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