Many binomial tables onlytabulate symmetries up to 0.5. This does not mean we cannot use thebinomial tables for any value of p greater than 0.5 – only thatsome manipulation is involved. The manipulation rests onthatrepresentsthe probability of success in most textbooks.
thenrepresents the probability of failure. If
then
andwe can use the tables with values of
Suppose we havewith
andwe want to find
Ifthere are
orless successes in
attempts,then there must be
ormore failures. We can represent the distribution of the number offailures in n attempts as
with
thenwe find
Wecan look up
inthe binomial tables so find
Suppose with the samedistribution that we want to findThereare
ormore successes so
orless failures. As before model the number of failures by
then
Wecan look up
inthe binomial tables.