A printing machine, capable of only printing the 10 digits, prints the right digit 12% of the time. Whenever the machine prints erroneously, all wrong possibilities are equally likely.

If a random key is pressed twice and a same digit comes out both times, what is the probability that it was the correct one?

Suppose we press "0" twice. The probability of geting two zeroes is 0.12²= 0.0144. The probability of getting other two equal digits is 9(0.88/9)²= 0.0860444.... Thus, the probability of getting the correct digit given that the same digit was printed twice is 0.0144/(0.0144+0.0860444...)= approximately 14.3%.

Posted by e.g. on 2006-07-19 11:53:11