Exams › JEE Advanced › Maths

A container holds four slips numbered 112, 121, 211, and 222. A single slip is picked randomly. Let A(i, where i = 1, 2, 3) represent the event that the ith digit of the chosen slip is 1. Which of the following is true?

1. The probabilities of A1, A2, and A3 are all equal.
2. The events A1, A2, and A3 are pairwise independent.
3. The events A1, A2, and A3 are pairwise independent but not mutually independent.
4. The probability of A1 is 1/2.

Correct answer: The probabilities of A1, A2, and A3 are all equal.

Solution

Each digit of the slips is equally likely to be 1, and the events A1, A2, and A3 have identical probabilities due to symmetry in the numbering of the slips. This makes the probabilities of A1, A2, and A3 equal.

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 →