Exams › JEE Advanced › Maths

A die is thrown three times, what is the likelihood that each subsequent roll shows a number greater than the one before?

1. 5/216
2. 5/54
3. 1/6
4. 5/36

Correct answer: 5/54

Solution

Each strictly increasing outcome corresponds to choosing 3 distinct values out of 6 in increasing order: C(6,3)=20 favourable cases out of 6^3=216 total. Probability = 20/216 = 5/54, option (b). The stored answer 1/6 is incorrect.

Related JEE Advanced Maths questions

• 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?
• Raj and Sanchita take turns rolling two dice until one of them achieves a total of 9. What could be the likelihood of Sanchita winning the game?

⚔️ Practice JEE Advanced Maths free + battle 1v1 →