Q. A box contains 4 red, 3 green, and 2 blue marbles. If a marble is drawn and it is green, what is the probability that the next marble drawn is red?
A.
0.4
B.
0.5
C.
0.6
D.
0.3
Solution
After drawing a green marble, there are 4 red, 2 green, and 2 blue marbles left. The probability of drawing a red marble next is 4/(4+2+2) = 4/8 = 0.5.
Q. A box contains 4 white and 6 black balls. If one ball is drawn at random, what is the probability that it is black given that it is not white?
A.
2/5
B.
3/5
C.
4/5
D.
1/5
Solution
The total number of balls is 10. The number of favorable outcomes (black balls) is 6. The probability that the ball is black given that it is not white is P(Black | Not White) = 6/6 = 1.
Q. A box contains 5 red, 3 blue, and 2 green balls. If one ball is drawn at random, what is the probability that it is blue given that it is not red?
A.
1/2
B.
1/4
C.
1/3
D.
1/5
Solution
The total number of balls that are not red is 5 (3 blue + 2 green). The probability that the ball is blue given it is not red is P(Blue | Not Red) = 3/5.
Q. A box contains 5 red, 3 green, and 2 blue marbles. If a marble is drawn and it is known to be red, what is the probability that it is the first marble drawn?
A.
1/5
B.
1/3
C.
1/2
D.
1/10
Solution
The probability of drawing a red marble is independent of the order. Therefore, P(First | Red) = 1/5.
Q. A box contains 5 red, 3 green, and 2 blue marbles. If a marble is drawn at random, what is the probability that it is green given that it is not red?
A.
1/2
B.
1/3
C.
1/4
D.
1/5
Solution
The total number of non-red marbles is 5 (3 green + 2 blue). Therefore, P(Green | Not Red) = 3/5.
Q. A box contains 5 red, 3 green, and 2 blue marbles. If one marble is drawn at random, what is the probability that it is green given that it is not red?
A.
1/2
B.
1/3
C.
1/4
D.
1/5
Solution
The total number of non-red marbles is 5 (3 green + 2 blue). The probability that the marble is green given that it is not red is P(Green | Not Red) = 3/5.
Q. A family has 3 children. What is the probability that at least one child is a girl given that at least one child is a boy?
A.
1/2
B.
2/3
C.
3/4
D.
1/4
Solution
The only combinations with at least one boy are: BBB, BBG, BGB, GBB, BGG, GBG, GGB. Out of these, all combinations except BBB have at least one girl. Thus, P(At least one girl | At least one boy) = 6/7.
Q. A student is selected at random from a class of 40 students, where 25 are boys and 15 are girls. What is the probability that the student is a boy given that the student is not a girl?
A.
1/2
B.
3/4
C.
5/8
D.
2/5
Solution
If the student is not a girl, they must be a boy. Therefore, P(Boy | Not Girl) = 1.
Q. A student is selected at random from a class of 40 students, where 25 are boys and 15 are girls. What is the probability that the student is a girl given that the student is not a boy?
A.
1/3
B.
1/2
C.
2/3
D.
3/4
Solution
The total number of students that are not boys is 15 (girls). The probability of selecting a girl given that the student is not a boy is 15/15 = 1.
Q. A student is selected at random from a group of 40 students, where 25 are studying Mathematics and 15 are studying Physics. What is the probability that the student is studying Mathematics given that they are not studying Physics?
A.
5/8
B.
3/8
C.
1/2
D.
1/3
Solution
If the student is not studying Physics, they must be studying Mathematics. Therefore, P(Math | Not Physics) = 1.
Q. A student is selected at random from a group of 40 students, where 25 are studying Mathematics and 15 are studying Physics. What is the probability that the student is studying Physics given that the student is not studying Mathematics?
A.
0
B.
1/3
C.
3/8
D.
1/2
Solution
If the student is not studying Mathematics, they must be studying Physics. Therefore, the probability is 1.
Q. A student is selected at random from a group of students who study Mathematics and Physics. If 70% study Mathematics and 40% study both subjects, what is the probability that a student studies Physics given that they study Mathematics?
A.
0.4
B.
0.3
C.
0.5
D.
0.6
Solution
Using the formula P(Physics|Mathematics) = P(Physics and Mathematics) / P(Mathematics) = 0.4 / 0.7 = 0.571.
Q. A student is selected from a class of 40 students, where 25 are girls and 15 are boys. What is the probability that the student is a girl given that the student is not a boy?
A.
1
B.
0
C.
1/2
D.
3/4
Solution
If the student is not a boy, they must be a girl. Therefore, the probability is 1.
Q. In a class of 30 students, 18 are boys and 12 are girls. If a student is selected at random, what is the probability that the student is a girl given that the student is not a boy?
A.
1/2
B.
2/3
C.
1/3
D.
1/4
Solution
The total number of students that are not boys is 12 (girls). The probability of selecting a girl given that the student is not a boy is 12/12 = 1.
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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