Question 1019204
a. (28+260)/400 = 18/25

b. (78+28)/400 = 53/200

c. The two events are mutually exclusive if P("non-smoker" and "absent less than 10 days") = 0. Since from the data, P("non-smoker" and "absent less than 10 days") = 260/400 = 13/20, the two events are NOT mutually exclusive.

d.  P("absent for less than 10 days"|smoker) =  P("absent for less than 10 days" AND smoker)/P(smoker) = {{{(34/400)/(7/25) = 17/56}}}

e.  P("absent for less than 10 days"|non-smoker) =  P("absent for less than 10 days" AND non-smoker)/P(non-smoker) = {{{(260/400)/(18/25) = 65/72}}}