Question

Four unit squares are chosen at random on a chessboard. What is the probability that three of them are of one colour and fourth is of opposite colour?

Answer 1

There are 32 squares of each colour arranged alternately. The probability of randomly selecting a dark square is the same probability as randomly selecting a light square, the probability being 1/2 in each case. The binomial distribution can be used to find the probability that three of them are of one colour and fourth is of opposite colour as follows:
\[P(3\ of\ one\ colour\ /\ one\ of\ the\ other)=4C3\times(\frac{1}{2})^{4}=\frac{4}{16}\]