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JEE Advanced 2023 Paper 2 Solutions

Paragraph for next two questions

Consider the

6 \times 6

square in the figure. Let

A_1, A_2, . . ., A_{49}

be the points of intersections (dots in the picture) in some order. We say that

A_i

and

A_j

are friends if they are adjacent along a row or along a column. Assume that each point

A_i

has an equal chance of being chosen.

Section: Mathematics

Question : 50 of 51

Marks: +1, -0

Let

p_i

i

i=0,1,2,3,4

X

i=0,1,2,3,4

P(X=i)=p_i

7 E(X)

Solution:

Number of points having 0 friend

=0

Number of points having 1 friend

=0

Number of points having 2 friends

=4

Number of points having 3 friends

=5 \times 4=20

Number of points having 4 friends

=49-24=25

\therefore

$p_i$	0	0	$\frac{4}{49}$	$\frac{20}{49}$	$\frac{25}{49}$
$X_i$	0	1	2	3	4

7(E(X))\;=7 \left(0+0+\; \frac{4}{49} \times 2+\; \frac{20}{49} \times 3+\; \frac{25}{49} \times 4\right)

\;= \left( \frac{100+60+8}{49} \right)

\;=24

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