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4) Conditional probability a) Consider the outcome of rolling two fair dice and define these two events: . F = Either die has the value of 4 . M = The sum of both dice is 6 What is the probability that either of the die has the value 4 given that the total sum of both dice is equal to 6? b) Suppose the university has designed a e-mail spam filter that attempts to identify spam by looking for commonly occurring phrases in spam. E-mail analysis has shown that 10% of email is spam, that the phrase "Large inheritance" appears in 5% of all emails, and that conditioned on being a spam email, 10% of those spam emails contain the phrase "Large inheritance". Suppose a new email is received containing the phrase "Large inheritance", what is the probability that it is spam? Start by defining these events: . M = the email is spam . L = the email contains the phrase "Large inheritance", and extracting P(M), P(L) and P( LIM ) from the statement above