A battery source in the Internal Revenue Service has stated that historically 90% of federal tax ...

  

A battery source in the Internal Revenue Service has stated that historically 90% of federal tax returns filed are free of arithmetic errors. A random sample of 25 returns are selected and checked carefully for arithmetic errors. Assuming independence, find the probability that:

a. All 25 returns are free of arithmetic errors. 

b. At most 23 returns are free of arithmetic errors. 

c. Fewer than 23 returns are free of arithmetic errors.