Class CBSE Class 12 Mathematics Probability Q #912
COMPETENCY BASED
APPLY
3 Marks 2023 SA
There are two coins. One of them is a biased coin such that P (head): P (tail) is 1:3 and the other coin is a fair coin. A coin is selected at random and tossed once. If the coin showed head, then find the probability that it is a biased coin.
Prev Next

AI Tutor Explanation

Powered by Gemini

Step-by-Step Solution

Let B be the event that the biased coin is selected, and F be the event that the fair coin is selected. Let H be the event that the coin shows heads.

We are given:

  • P(H|B) = 1/4 (Probability of getting heads given the biased coin is selected)
  • P(H|F) = 1/2 (Probability of getting heads given the fair coin is selected)
  • P(B) = 1/2 (Probability of selecting the biased coin)
  • P(F) = 1/2 (Probability of selecting the fair coin)

We want to find P(B|H), the probability that the coin is biased given that it showed heads. We can use Bayes' Theorem:

P(B|H) = [P(H|B) * P(B)] / [P(H|B) * P(B) + P(H|F) * P(F)]

Substitute the given values:

P(B|H) = [(1/4) * (1/2)] / [(1/4) * (1/2) + (1/2) * (1/2)]

P(B|H) = (1/8) / (1/8 + 1/4)

P(B|H) = (1/8) / (1/8 + 2/8)

P(B|H) = (1/8) / (3/8)

P(B|H) = 1/3

Correct Answer: 1/3

AI generated content. Review strictly for academic accuracy.

Pedagogical Audit
Bloom's Analysis: This is an APPLY question because the student needs to apply the concepts of conditional probability and Bayes' theorem to solve the problem. They must use the given information to calculate the required probability.
Knowledge Dimension: PROCEDURAL
Justification: The question requires the student to follow a specific procedure (Bayes' Theorem) to calculate the conditional probability. The student needs to apply the formula correctly and perform the necessary calculations.
Syllabus Audit: In the context of CBSE Class 12, this is classified as COMPETENCY. The question assesses the student's ability to apply the concepts of probability to a real-world scenario involving biased and fair coins, requiring them to use Bayes' theorem.

More from this Chapter

SA
The probability distribution of a random variable X is given below : $$\begin{array}{|c|c|c|c|} \hline X & 1 & 2 & 3 \\ \hline P(X) & \frac{k}{2} & \frac{k}{3} & \frac{k}{6} \\ \hline \end{array}$$ (i) Find the value of $k$. (ii) Find $P(1\le X
VSA
10 identical blocks are marked with '0' on two of them, '1' on three of them, '2' on four of them and '3' on one of them and put in a box. If X denotes the number written on the block, then write the probability distribution of X and calculate its mean.
SA
For the vacancy advertised in the newspaper, 3000 candidates submitted their applications. From the data it was revealed that two third of the total applicants were females and other were males. The selection for the job was done through a written test. The performance of the applicants indicates that the probability of a male getting a distinction in written test is 0.4 and that a female getting a distinction is 0.35. Find the probability that the candidate chosen at random will have a distinction in the written test.
SA
The probability distribution for the number of students being absent in a class on a Saturday is as follows: X: 0, 2, 4, 5; $P(X)$: p, 2p, 3p, p. Where X is the number of students absent. (i) Calculate p. (ii) Calculate the mean of the number of absent students on Saturday.
SUBJECTIVE
(i) A person was tested randomly. What is the probability that he/she has contracted the disease ? (ii) Given that the person has not contracted the disease, what is the probability that the person is from category $A_2$ ?
View All Questions