ProbabilityHardBloom L3
Question
If two squares are chosen at random on a chess board, then find the probability so that
Options
A.they have a side common is $\frac{1}{9}$
B.they have a side common is $\frac{1}{18}$
C.they have contact at a corner is $\frac{7}{144}$
D.they have contact at a corner is $\frac{7}{72}$
Solution
Sol. [Key Concept: Two squares on a chessboard: split into same-row, same-column and diagonal cases.]
(a) $\frac{7 \times 8 + 7 \times 8}{\ ^{64}C_{2}} = \frac{7 \times 8 \times 2 \times 2}{64 \times 63} = \frac{1}{18}$
(b) $p = \frac{7 \times 7 + 7 \times 7}{\ ^{64}C_{2}} = \frac{2 \times 7 \times 7 \times 2}{64 \times 63} = \frac{7}{144}$
Alternate: (a)
$$= \frac{1 + 9 + 1}{8 \times 63} = \frac{1 + 9 + 1}{2 \times 9} = \frac{1}{18}$$
(b) $\frac{36 \times 4 + 24 \times 2 + 4 \times 1}{64 \times 63} = \frac{7}{144}$
Create a free account to view solution
View Solution FreeMore Probability Questions
A tetrahedral fair dice whose faces are numbered $1,2,3$ and 4 . The die is thrown and the face on which the pyramid lan...From $(4\text{ }m + 1)$ tickets numbered as $1,2,3,\ldots.,4\text{ }m + 1$; three tickets are chosen at random. Then the...In a multiple-choice question, there are 4 alternative answers of which one or more may be correct. A candidate will get...An urn contains 5 white and 3 black balls and 4 balls are drawn at random. The probability of getting white and black ba...A and B throw two dice, if A throws 8, the probability that B will throw a higher number is-...