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Saturday, 31 October

JEE Main 2021 · MathsNumerical answerNumerical valueHardMulti-step

JEE Main 17 March 2021, Shift 1, Maths Q88

Question 88 of 90 in this shift, Maths question 28 of 30, Section B.

Let 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 β\beta and only E3E_3 occurs is γ\gamma. Let ‘p’ denote the probability of none of events occurs that satisfies 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 given probabilities are assumed to lie in the interval (0,1)(0, 1). Then, Probability of occurrence of E1Probability of occurrence of E3\frac{\text{Probability of occurrence of }E_1}{\text{Probability of occurrence of }E_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. 24 Feb 2021, Shift 1 · Q82Let 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…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.