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Unformatted text preview: ith a probability p. Because the points are placed placed in the specified cell. However, because in total r points are placed in the grid, for a specified cell to contain m points the complementary event (points not landing in the desired cell) must have occurred r-m times, each time with a probability q. Therefore, the probability of a single sequence occurring with m points being placed in the specified cell is given by (17) (ii) Binomial Coefficients Binomial coefficients are combinational numbers which define the total number of different sequences in which an event can occur exactly m times in r trials on an experiment. For example, it is easy to see that there are 6 sequences in which 2 heads can occur in 4 tosses of a coin, these are HHTT HTTH HTHT TTHH THHT THTH In this case the answer was obtained by experimentation, however, the general solution for the number of sequences in which an event occurs m times in r trials is given by the binomial coefficient. Formally this is expressed as (14) (18)
If we evaluate thi...
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