In this year's Pre-Health program there are 335 students. Of the 335, there are 232 considering going into a nursing program, 130 considering going into a paramedic program, and 67 are considering both.

a) Draw a Venn Diagram to illustrate the sample space. Be sure to include the students that are not considering either of these programs.

b) Are the events "considering going into a nursing program" and "considering going into a paramedic program" mutually exclusive?

c) Determine the probability that a student is considering going into either a nursing program or paramedic program.

d) Determine the probability that a randomly selected student is not considering going into either a nursing program or paramedic program.

e) Determine the probability that a randomly selected student is considering going into both a nursing program and a paramedic program.

f) Determine the probability that a randomly selected student is considering going into the nursing program given that they are considering going into the paramedic program.