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Saturday, 31 October

JEE Main 2021 · MathsNumerical answerNumerical valueHardMulti-step

JEE Main 24 February 2021, Shift 1, Maths Q82

Question 82 of 90 in this shift, Maths question 22 of 30, Section B.

Let BiB_i (i=1,2,3i = 1, 2, 3) be three independent events in a sample space. The probability that only B1B_1 occur is α\alpha, only B2B_2 occurs is β\beta and only B3B_3 occurs is γ\gamma. Let p be the probability that none of the events BiB_i occurs and these 4 probabilities satisfy the equations (α−2β)p=αβ(\alpha - 2\beta)p = \alpha\beta and (β−3γ)p=2βγ(\beta - 3\gamma)p = 2\beta\gamma (All the probabilities are assumed to lie in the interval (0,1)(0, 1)). Then P(B1)P(B3)\frac{P(B_1)}{P(B_3)} is equal to ___________.

Official answer

6

NTA final key.

Chapter
Probability
Topic
Conditional Probability
Idea tested
Independence Criterion

Same idea in other shifts

Asked 5× in all
  1. 31 Jan 2024, Shift 1 · Q19Two marbles are drawn in succession from a box containing 10 red, 30 white, 20 blue and 15 orange marbles, with replacement being made…EasySingle correct
  2. 25 Jun 2022, Shift 1 · Q10Let E1E_1 and E2E_2 be two events such that the conditional probabilities P(E1∣E2)=12P(E_1|E_2)=\frac{1}{2}, P(E2∣E1)=34P(E_2|E_1)=\frac{3}{4} and…MediumSingle correct
  3. 4 Aug 2021, Shift 1 · Q77Four persons work independtly of each other on a task. If the probabilities that they will complete the task are :…EasySingle correct
  4. 17 Mar 2021, Shift 1 · Q88Let there be three independent events E1E_1, E2E_2 and E3E_3. The probability that only E1E_1 occurs is α\alpha, only E2E_2 occurs is…HardNumerical value

Question text from the official JEE Main paper published by NTA; answer from the final answer key. Chapter, topic and idea tags, difficulty and skill are Lumi’s. Lumi analyses 108 of the 174 JEE Main shifts held from 2017 to 2026.