First slide

Theorems of probability

Question

Two squares are chosen at random on a chess board. The probability that they have a side in common is

Moderate

A

$\frac{1}{9}$
B

$\frac{2}{7}$
C

$\frac{1}{18}$
D

$\frac{1}{3}$

Solution

$n (S) = 64_{C_{2}} = 32 \times 63$

$t h e n u m b e r o f w a y s o f s e l e c t i n g t w o s q a u r e s f o r w h i c h o n e s i d e i s c o m m o n i n a r o w i s \to 7 w a y s$

$F o r 8 r o w s \to 7 \times 8 = 56 w a y s$

Similarly   $f o r 8 c o l u m n s = 56 w a y s$

$∴ n (E) = 56 + 56 = 112$
$P (E) = \frac{2 \times 56}{32 \times 63} = \frac{1}{18}$ .

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