Exams › JEE Advanced › Maths
Three urns X, Y, and Z contain the following balls: X has 7 red and 5 black balls; Y has 5 red and 7 black balls; Z has 6 red and 6 black balls. One urn is chosen at random (each with equal probability) and a single ball is drawn from it. Given that the drawn ball is black, what is the probability that it came from urn X?
- 4/17
- 5/18
- 7/18
- 5/36
Correct answer: 5/18
Solution
By Bayes' theorem: P(X|black) = (5/12 * 1/3) / (1/2) = (5/36) / (1/2) = 10/36 = 5/18.
Related JEE Advanced Maths questions
- A die is thrown three times, what is the likelihood that each subsequent roll shows a number greater than the one before?
- A number x is randomly selected from the first 100 positive integers. What is the probability that the inequality (x² - 60x + 800) / (x - 30) < 0 holds true?
- From a sequence of 3n consecutive integers, three numbers are picked randomly. What is the probability that their total is a multiple of 3?
- Ten individuals are seated around a circular table with chairs numbered from 1 to 10. What is the likelihood that two specific individuals, A and B, always sit next to each other?
- The likelihoods of three events X, Y, and Z are P(X) = 0.6, P(Y) = 0.4, and P(Z) = 0.5. If P(X ∪ Y) = 0.8, P(X ∩ Z) = 0.3, P(X ∩ Y ∩ Z) = 0.2, and P(X ∪ Y ∪ Z) ≥ 0.85, then which of the following is true?
- A keyring contains 'n' keys, with only one being the correct key to unlock a lock. A person attempts to unlock the lock by trying keys randomly, discarding each key after it has been tried. If the probability of successfully unlocking the lock on the kᵗʰ attempt is P, which of the following statements is accurate?
⚔️ Practice JEE Advanced Maths free + battle 1v1 →