8 points Show your answers in the boxes provide. Supporting work/calculations should appear below the answer to part (c). Numerical answers with no visible supporting work will NOT receive full credit. Several common words are known to appear in spam e-mails, such as "miracle", "instant", "obligation", "undisclosed", "giveaway". Suppose that 1 in every 12 messages s spam for an email account. An email that is not spam is termed as ham. Assume that for spam messages, the proportion of messages that include the above-listed words in email are as follows: Miracle 0.045 Instant 0.034 Obligation 0.014 Undisclosed 0.014 Giveaway 0.051 Assume that for ham messages, the proportion of messages that include these words are as follows: Miracle 0.0022 nstant 0.0022 Obligation 0.0041 Undisclosed 0.0011 Giveaway 0.0015 X a) If a message includes the word "instant", what is the probability the message is spam? Answer if a message includes the word "instant", what is the probability the message is ham? Answer C) Should messages that include the word "instant" be flagged as spam? Why or why not? (1-2 sentences is adequate) Answer Supporting Work