# Email filtering programs

## Question

Suppose there are two programs running in your email client used to combat spam. Both programs analyze each email and mark it as either legitimate (L) or spam (S). You can assume that 10% of the email in your inbox is legitimate and that the two programs are each 90% accurate in identifying spam. Also, you can assume the outputs of the two programs are conditionally independent.

Given this information, find the probability that the email is legitimate, given that the 1st program marks it as legitimate.