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.

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
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   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
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   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
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   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
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   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
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   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.

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