The probability of a successful optical alignment in the ass

The probability of a successful optical alignment in the assembly of an optical storage product is 0.8. Assuming the trials are independent, what is the probability that the first successful alignment requires exactly three trials?

Solution

P( First succesful required 3 trials) = P( 2 Fail) * P( Success) = 0.2 * 0.2 * 0.8 = 0.032