JEE Main 2021 (Online) 20th July Evening Shift | Probability Question 103 | Mathematics

Let A, B and C be three events such that the probability that exactly one of A and B occurs is (1 $$-$$ k), the probability that exactly one of B and C occurs is (1 $$-$$ 2k), the probability that exactly one of C and A occurs is (1 $$-$$ k) and the probability of all A, B and C occur simultaneously is k², where 0 < k < 1. Then the probability that at least one of A, B and C occur is :

greater than $${1 \over 8}$$ but less than $${1 \over 4}$$

greater than $${1 \over 2}$$

greater than $${1 \over 4}$$ but less than $${1 \over 2}$$

exactly equal to $${1 \over 2}$$

JEE Main 2021 (Online) 20th July Morning Shift

MCQ (Single Correct Answer)

-1

Words with or without meaning are to be formed using all the letters of the word EXAMINATION. The probability that the letter M appears at the fourth position in any such word is :

$${1 \over {66}}$$

$${1 \over {11}}$$

$${1 \over {9}}$$

$${2 \over {11}}$$

JEE Main 2021 (Online) 20th July Morning Shift

MCQ (Single Correct Answer)

-1

The probability of selecting integers a$$\in$$[$$-$$ 5, 30] such that x² + 2(a + 4)x $$-$$ 5a + 64 > 0, for all x$$\in$$R, is :

$${7 \over {36}}$$

$${2 \over {9}}$$

$${1 \over {6}}$$

$${1 \over {4}}$$

JEE Main 2021 (Online) 18th March Evening Shift

MCQ (Single Correct Answer)

-1

Out of Syllabus

Let in a Binomial distribution, consisting of 5 independent trials, probabilities of exactly 1 and 2 successes be 0.4096 and 0.2048 respectively. Then the probability of getting exactly 3 successes is equal to :

$${{40} \over {243}}$$

$${{128} \over {625}}$$

$${{80} \over {243}}$$

$${{32} \over {625}}$$

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