JEE Advanced 2026 Paper 1 Online

MCQ (More than One Correct Answer)

-1

Suppose that Box I contains 6 red balls and 9 green balls, and Box II contains 8 red balls and 12 green balls. All the balls of Box I and Box II are mixed together and a ball is chosen at random from them. Let $E_1$ be the event that the ball chosen belonged to Box I and let $E_2$ be the event that the ball chosen belonged to Box II. Let $F_1$ be the event that the ball chosen is red and let $F_2$ be the event that the ball chosen is green.

Then which of the following statements is (are) TRUE?

The events $E_1$ and $F_1$ are independent

The events $E_2$ and $F_2$ are dependent

The conditional probability $P(F_1|E_1)$ is equal to the conditional probability $P(F_1|E_2)$

The conditional probability $P(F_1|E_1)$ is greater than the conditional probability $P(F_2|E_2)$

JEE Advanced 2021 Paper 1 Online

MCQ (More than One Correct Answer)

-2

Let E, F and G be three events having probabilities $$P(E) = {1 \over 8}$$, $$P(F) = {1 \over 6}$$ and $$P(G) = {1 \over 4}$$, and let P (E $$\cap$$ F $$\cap$$ G) = $${1 \over {10}}$$. For any event H, if H^c denotes the complement, then which of the following statements is (are) TRUE?

$$P(E \cap F \cap {G^c}) \le {1 \over {40}}$$

$$P({E^c} \cap F \cap G) \le {1 \over {15}}$$

$$P(E \cup F \cup G) \le {{13} \over {24}}$$

$$P({E^c} \cup {F^c} \cup {G^c}) \le {5 \over {12}}$$

JEE Advanced 2019 Paper 1 Offline

MCQ (More than One Correct Answer)

-1

There are three bags B₁, B₂ and B₃. The bag B₁ contains 5 red and 5 green balls, B₂ contains 3 red and 5 green balls, and B₃ contains 5 red and 3 green balls. Bags B₁, B₂ and B₃ have probabilities $${3 \over {10}}$$, $${3 \over {10}}$$ and $${4 \over {10}}$$ respectively of being chosen. A bag is selected at random and a ball is chosen at random from the bag. Then which of the following options is/are correct?

Probability that the chosen ball is green, given that the selected bag is B₃, equals $${3 \over 8}$$.

Probability that the selected bag is B₃, given that the chosen ball is green, equals $${5 \over 13}$$.

Probability that the chosen ball is green equals $${39 \over 80}$$.

Probability that the selected bag is B₃ and the chosen ball is green equals $${3 \over 10}$$.

JEE Advanced 2017 Paper 1 Offline

MCQ (More than One Correct Answer)

-1

Let X and Y be two events such that $$P(X) = {1 \over 3}$$, $$P(X|Y) = {1 \over 2}$$ and $$P(Y|X) = {2 \over 5}$$. Then

$$P(Y) = {4 \over {15}}$$

$$P(X'|Y) = {1 \over 2}$$

$$P(X \cup Y) = {2 \over 5}$$

$$P(X \cap Y) = {1 \over 5}$$

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