An email spam filter checks an incoming email for a list of key words. If enough of these key words are present, then the email is automatically sent to the spam folder. The filter is 95% accurate in correctly identifying a spam email, but will incorrectly send a non-spam email to the spam folder with probability 0.5%. Previous data suggests that 4% of emails are spam emails.
A) What is the probability that a randomly selected email will be labelled as spam?
B) Use your result from A to determine the probability that an email which has not been identified as spam is actually a spam email.
C) The developers of the spam filter wish to reduce the probability in part B to 0.1%. What should the probability of the filter correctly identifying a spam email be increased to so that this objective is reached?