Statistics and Data Analysis for Microarrays Using R and Bioconductor, 2nd Edition

Probability distributions 281

B not B total

A k m-k m

not A

total n N-n N

FIGURE 9.1 4: There are



n

k



ways to pick k objects with property B fr om

the set of n objects with property B. For any such choice, there will be m −k

objects with property A but not B. The number of different combinations of

m −k objects with A but not B picked from N −n objects is



N−n

m−k



. Overall,

there a re



n

k



·



N−n

m−k



favorable cases (with exactly k successes) out of a total

number of



N

m



which yields the probability shown in E q. 9.28.

can be swapped. In consequence, the hypergeometric probability can also cal-

culated reasoning on the other direction of the table, as illustra ...