Define and frame
Compute the probability of two heads in two independent fair-coin flips. Does observing two heads change the probability of heads on the third flip?
Scenario: Compare a fair-coin problem with conditional medical-test probabilities. State the modelling assumptions explicitly.
Use the fictional dataset if the question refers to it. Always show your reasoning; an exact number without context is not enough. The four written tasks are teacher-assessed. The self-check below is formative and does not affect the 20-mark assignment.
Written problem set
Calculate or apply
Suppose 20 of 100 participants are in group A, and eight of those show event B. Compute P(B|A). Why does this not give P(A|B)?
Evaluate the design
A screening test has 1% prevalence, 90% sensitivity and 95% specificity. Find expected true positives and false positives among 10,000 people.
Interpret and communicate
Explain why a coin outcome is not “due” after a streak, using independence.
Standard scoring guide
Each written task is worth 5 points: correct key idea (2), justified application or computation (2), and a clear statement with limits (1). This original rubric is not official UCL assessment.
Formative self-check · 4 questions
Choose one answer for each item, then check the feedback. Answers and explanations are available on this public study page; the separate written-task instructor key is private.