Session 07-09 - Oral Exam Practice III

Section 07: Probability & Statistics

Dr. Nikolai Heinrichs & Dr. Tobias Vlćek

Welcome

Oral Practice, Round Three

By now the format is familiar - the topics are not

  • Groups of three, rotating candidate / examiner / observer roles
  • Block A: 30 minutes preparation, free-speech presentation, follow-ups at levels [I]-[III]
  • Block B: spontaneous impulse from a different area
  • Format reference: oral exam guide

Today’s Topic Sets

Sets 12, 14 and 16 - handed out in class

  • Set 12: Probability & statistics (contingency table, Bayes) · Cost & profit (quadratic, break-even)
  • Set 14: Graphical calculus (reasoning from \(f'\)) + systems · Probability (combinatorics)
  • Set 16: Binomial distribution, “at least one” · Logarithmic function analysis
  • Probability is fresh from this section - perfect timing to explain it aloud

Focus of This Round

Surviving Block B

This round’s training goal: the spontaneous block

  • You get no preparation - and that is fine; the examiner expects thinking, not polish
  • Classify first: “This is a conditional-probability situation, so I’ll draw a tree.”
  • Standard openers you can always reach for: a tree diagram, a table, a sketch
  • Speak while you draw - silence is the only real mistake

Explaining Probability Well

  • Always name the model: “Drawing without replacement, so probabilities change.”
  • Distinguish clearly: \(P(A \mid B)\) is not \(P(B \mid A)\) - say what is given
  • “At least one” → work with the complement, and say why
  • Round sensibly and interpret: “About 8% of tested parts are false positives.”

Practice Rounds

Rounds One and Two

  • Preparation: 30 minutes - examiners study their key, observers prepare a feedback sheet
  • Exam conversation: ~20 minutes, Block B gets at least 7 of them today
  • Feedback: 10 minutes - focus on how the candidate handled the unprepared block
  • Rotate roles and sets for round two

Coffee Break - 15 Minutes

Final Round

Round Three

Everyone has now faced a spontaneous Block B three times

  • Final rotation - examiners, escalate to level [III] questions where you can
  • Observers: note whether answers interpret results, not just compute them

Wrap-Up

Key Takeaways

  • Block B is won by classifying the problem and reaching for a standard tool
  • Trees, tables, and complements carry almost every probability conversation
  • Your explanation gaps here are also your written-exam gaps - same study list
  • The final dress rehearsal comes in the exam-preparation section

Next Session Preview

Session 08-01: Compound Interest & Geometric Sequences

  • We start Section 08: Financial Mathematics
  • Interest, growth factors, and the geometric series behind them

Preparation

Pick the probability topic that felt shakiest out loud and rework it in writing.