JEE Advanced 2026 · Paper 1 · Mathematics Q5

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MathematicsMultiple correct+4 / -1Question 5 of 48

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\mid E_1)

is equal to the conditional probability

P(F_1\mid E_2)

The conditional probability

P(F_1\mid E_1)

is greater than the conditional probability

P(F_2\mid E_2)

Answer and worked solution

Official answer: A, C

There are 35 balls: 15 from Box I, 20 from Box II; 14 red, 21 green.

(A) $P(E_1\cap F_1)=\frac6{35}$ and $P(E_1)P(F_1)=\frac{15}{35}\cdot\frac{14}{35}=\frac{6}{35}$ . Equal, so independent. True.

(B) If $E_1,F_1$ are independent, so are their complements $E_2,F_2$ . False.

(C) $P(F_1\mid E_1)=\frac6{15}=\frac25$ and $P(F_1\mid E_2)=\frac8{20}=\frac25$ . True.

(D) $P(F_2\mid E_2)=\frac{12}{20}=\frac35>\frac25$ . False.

Topics:Independent events Conditional probability

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JEE Advanced 2026 · Paper 1, Mathematics question 5