Question

On a standard 8×8 chessboard (alternating black and white squares), label the rows and columns 1,...,8. You pick a square at random. Are these events independent. (a) A = {white square}; B = {black square}. (b) A = {even row}; B = {even column}. (c) A = {white square}; B = {even column}.

Answer 1

Answer: Only option 'a' are independent events.

Explanation:

Since we have given that

8 × 8 chess board.

(a) A = {white square}; B = {black square}.

Since no white squares can be black squares.

So, A and B are independent events .

(b) A = {even row}; B = {even column}.

There is possibilities of even row and even column both.

i.e. (2,2) (2,4) etc.

So, A and B are not dependent.

(c) A = {white square}; B = {even column}.

Since there are possibilities of white square of even column.

W2, W4, W6, W8

So, they are not independent.

Hence, only option 'a' are independent events.