Q. In a class of 40 students, 25 are girls and 15 are boys. If a student is selected at random, what is the probability that the student is a boy given that the student is not a girl?
A.
1
B.
0.5
C.
0.25
D.
0.75
Solution
If a student is not a girl, they must be a boy. Therefore, P(Boy | Not Girl) = 15/15 = 1.
Q. In a class of 40 students, 25 are taking Mathematics, 15 are taking Physics, and 10 are taking both. What is the probability that a student is taking Physics given that they are taking Mathematics?
Q. In a family with 3 children, what is the probability that at least one child is a girl given that at least one child is a boy?
A.
0.75
B.
0.5
C.
0.25
D.
0.6
Solution
The total outcomes for 3 children are 8. The outcomes with at least one boy are 7. The outcomes with at least one girl and one boy are 6. Thus, P(Girl|Boy) = 6/7 ≈ 0.857.
Q. In a group of 100 people, 60 like cricket, 30 like football, and 10 like both. What is the probability that a person likes football given that they like cricket?
Q. In a group of 100 people, 60 like football, 30 like basketball, and 10 like both. What is the probability that a person likes football given that they like basketball?
A.
0.5
B.
0.3
C.
0.6
D.
0.7
Solution
Using conditional probability, P(Football | Basketball) = P(Football and Basketball) / P(Basketball) = 10/30 = 1/3.
Q. In a group of 50 people, 20 are smokers and 30 are non-smokers. If a person is selected at random, what is the probability that the person is a non-smoker given that they are not a smoker?
A.
1
B.
0
C.
1/2
D.
1/3
Solution
If the person is not a smoker, they must be a non-smoker. Therefore, the probability is 1.
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.
Conditional Probability is a crucial concept in statistics and probability theory that plays a significant role in various examinations. Understanding this topic not only enhances your analytical skills but also boosts your performance in exams. Practicing MCQs and objective questions on Conditional Probability helps you grasp the concepts better and prepares you for important questions that frequently appear in school and competitive exams.
What You Will Practise Here
Definition and basic concepts of Conditional Probability
Formulas and theorems related to Conditional Probability
Applications of Conditional Probability in real-life scenarios
Bayes' Theorem and its significance
Understanding independent and dependent events
Solving Conditional Probability problems with step-by-step solutions
Diagrams and visual aids to illustrate concepts
Exam Relevance
Conditional Probability is a vital topic in various educational boards including CBSE and State Boards, as well as competitive exams like NEET and JEE. Students can expect questions that test their understanding of the basic principles, application of formulas, and real-world problem-solving. Common question patterns include multiple-choice questions that require you to calculate probabilities based on given conditions, making it essential to practice thoroughly.
Common Mistakes Students Make
Confusing conditional probability with joint probability
Misapplying Bayes' Theorem in problem-solving
Overlooking the importance of event independence
Failing to interpret the conditions correctly in word problems
FAQs
Question: What is Conditional Probability? Answer: Conditional Probability is the probability of an event occurring given that another event has already occurred.
Question: How is Bayes' Theorem related to Conditional Probability? Answer: Bayes' Theorem provides a way to update the probability of a hypothesis based on new evidence, using Conditional Probability.
Now is the time to enhance your understanding of Conditional Probability! Dive into our practice MCQs and test your knowledge to excel in your exams. Remember, consistent practice is the key to success!
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