JEE Advanced · 2023 · 04 Jun 2023 · Paper 2 · Probability

Passage

Consider the

6 \times 6

square in the figure. Let

A_{1}, A_{2}, \dots, 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.

Consider the

6 \times 6

square in the figure. Let

A_{1}, A_{2}, \dots, 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.

Two distinct points are chosen randomly out of the points

A_{1}, A_{2}, \dots, A_{49}

. Let

p

be the probability that they are friends. Then the value of

7 p

Answer: 0.5

Solution

Total ways to choose 2 points:

(2 49) = \frac{49 \times 48}{2} = 1176

Number of adjacent pairs (friends):

p = \frac{84}{1176} = \frac{84}{1176} = \frac{1}{14}

7 p = 7 \times \frac{1}{14} = \frac{1}{2} = 0.5

JEE Advanced · 2023 · 04 Jun 2023 · Paper 2 · Numerical answer