Complex BINOMDIST function

       ---A---- ---B---- ---C---- ----------------D----------------
   1   Subjects Failures   Prob                                    
   2        100       25 0.999996 C2: =BINOMDIST(B2, A2, 10%, TRUE)
   3         99       24 0.999989                                  
   4         98       23 0.999972                                  
   5         97       22 0.999931                                  
   6         96       21 0.999832                                  
   7         95       20 0.999606                                  
   8         94       19 0.999106                                  
   9         93       18 0.998042                                  
  10         92       17 0.995869                                  
  11         91       16 0.991618                                  
  12         90       15 0.983675                                  
  13         89       14 0.969555                                  
  14         88       13 0.945758                                  
  15         87       12 0.907898                                  
  16         86       11 0.851326                                  
  17         85       10 0.772388                                  
  18         84        9 0.670233                                  
  19         83        8 0.548620                                  
  20         82        7 0.416751                                  
  21         81        6 0.288098                                  
  22         80        5 0.176917                                  
  23         79        4 0.093530                                  
  24         78        3 0.040754                                  
  25         77        2 0.013690                                  
  26         76        1 0.003145                                  
  27         75        0 0.000370

The formula for the first line calculates the probability of having at most at most 25 failures in 100 trials when the probability of failure is 10%.

For 89 subjects (trials), the probability of at most 14 failures (leaving 75) is 96.9%