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Detection result shows that 40% of the entire emails are spam. Therefore, we need to design software that will be used to filter spam emails.

Detection result shows that 40% of the entire emails are spam. Therefore, we need to design software that will be used to filter spam emails. One of the software firms claims that they have developed software that is able to detect 95% of spam emails, and the probability for a false positive rate (i.e., a non-spam email is detected as spam) is 5%.

If the designed software is detected as spam, then what is the probability of having non-spam email?

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