Bayes Theorem Quiz - CBSE Class 12 Mathematics

Free practice quiz: Bayes Theorem (CBSE Class 12 Mathematics). 16 multiple-choice questions with answers and explanations. Play online, no sign-up needed.

This CBSE Class 12 Mathematics practice quiz has 16 multiple-choice questions on Bayes Theorem, and 16 of them come with an explanation. Try the 5 sample questions below (tap an option to check yourself), then play the full quiz online. No sign-up needed.

Sample questions

1. If a box contains 3 red balls and 2 blue balls, what is the probability of drawing a blue ball?

   1. 2/5
   2. 1/2
   3. 3/5
   4. 1/5
   Show answer

   Answer: A. 2/5

   The probability of drawing a blue ball is calculated as the number of blue balls divided by the total number of balls. There are 2 blue balls and a total of 5 balls, so the probability is 2/5.

2. A box contains 4 green balls and 1 yellow ball. What is the probability of selecting a yellow ball if one ball is randomly selected?

   1. 1/5
   2. 1/4
   3. 4/5
   4. 0
   Show answer

   Answer: A. 1/5

   To find the probability of selecting the yellow ball, divide the number of yellow balls by the total number of balls. There is 1 yellow ball and a total of 5 balls, leading to a probability of 1/5.

3. In a lottery game, the probability of winning is 0.1. If a person plays the game 5 times, what is the probability that they will win at least once?

   1. 0.41
   2. 0.5
   3. 0.9
   4. 0.1
   Show answer

   Answer: A. 0.41

   To find the probability of winning at least once when the probability of winning is 0.1, calculate the complement of losing all 5 times. The probability of losing once is 0.9, so of losing 5 times is 0.9^5 = 0.59049. The probability of winning at least once is then 1 - 0.59049 = approximately 0.41.

4. A factory produces 3 defective items for every 10 items produced. If a random sample of 15 items is selected, what is the probability that exactly 2 of them are defective?

   1. 0.207
   2. 0.144
   3. 0.237
   4. 0.186
   Show answer

   Answer: A. 0.207

   This follows the binomial probability formula. The probability of getting exactly k successes in n trials is given by P(X = k) = (n choose k) p^k (1-p)^(n-k). Substituting n = 15, k = 2, and p = 0.3 gives approximately 0.207.

5. If you flip a coin 10 times, what is the probability of getting exactly 5 heads?

   1. 0.246
   2. 0.5
   3. 0.200
   4. 0.132
   Show answer

   Answer: A. 0.246

   The probability of getting exactly k heads in n flips is given by the binomial formula. Here, n = 10, k = 5, and p = 0.5. After calculations, the probability is approximately 0.246.

More questions in this quiz

Answers and explanations are in the full quiz.

1. What is the probability of drawing a red ball from the box mentioned above?
2. In a disease screening test, the probability of having the disease is 0.02. If a test is 90% accurate, what is the probability of a positive test result given that the person has the disease?
3. If the probability of event A is 0.3 and the probability of event B is 0.7, what is the probability of both A and B occurring if they are independent?
4. A student is selected at random from a group of students. The probability that the student is a boy is 0.6. What is the probability that the student is a girl?
5. What is the Bayes' theorem formula for revising probabilities?
6. Suppose a box contains 4 red balls and 6 blue balls. If one ball is drawn at random, what is the probability that the ball is red given that it is not blue?
7. Given that the probability of event A is 0.1 and event B is independent with a probability of 0.5, what is the probability that either A or B occurs?
8. If the probability that a randomly chosen student passes an exam is 0.8, what is the probability that at least one of 6 students passes the exam?
9. In a game, if the probability of winning is 0.6, what is the probability of winning at least 3 out of 5 games?
10. What is the posterior probability if the prior probability is 0.2, likelihood is 0.9, and marginal likelihood is 0.5?
11. If the 95% confidence interval for a population mean is (40, 60), what does this imply about the mean?

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