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IB Maths AI SL 4.7 Discrete Random Variables Questions

Practise constructing discrete probability distributions, checking probabilities sum to one, calculating expected value and judging fairness or long-run outcomes.

Syllabus
First assessment 2021
Course
Mathematics: applications and interpretation SL
Level
SL

Exam points

  • Construct or interpret a discrete probability distribution and calculate its expected value/mean.
  • Use expected value to assess a game, decision or long-run outcome, including fairness when E(X)=0.
  • Check probabilities sum to one and explain the contextual meaning of the distribution.

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Study SL 4.7—Discrete random variables conceptsOpen the corresponding Concept lesson for explanations, examples and exam connections.

IB Maths AI SL 4.7 Discrete Random Variables Questions question 1

[Maximum number: 2]

A large international sports tournament tests their athletes for banned substances.
They interpret a positive test result as meaning that the athlete uses banned substances. A negative result means that they do not.
The probability that an athlete uses banned substances is estimated to be 0.06 .
If an athlete uses banned substances, the probability that they will test positive is 0.71 .
If an athlete does not use banned substances, the probability that they will test negative is 0.98 .

A random sample of 1300 athletes at the tournament are selected for testing. Calculate the expected number of athletes in the sample that will receive an incorrect test result.

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