You are attempting to determine the probability that incoming messages are spam, based on whether each contains the word 'account'. For each message, consider two states, s1 (spam) and s2 (NOT spam). The overall probability that a message is spam is P(s1)=0.1, so P(s2)=0.9. Many spam messages contain the word 'account', so P(account|s1)=0.3. There are, of course, legitimate emails that contain the word 'account', so P(account|s2)=0.04. Using this information, calculate the probabilities in this and the following questions.

1.)What is the joint probability P(s1 and account)?

2.) What is the joint probability P(s2 and account)?

3.) What is the probability P(account)?

4.) What is the posterior probability P(s1|account)?

5.) What is the posterior probability P(s2|account)?