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IB Maths AI SL 4.8 Binomial Distribution Questions

Practise choosing a binomial model, identifying n and p, calculating probabilities, mean or variance with technology, and checking assumptions in context.

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

Exam points

  • Choose the binomial model and identify n and p for a fixed number of independent trials with two outcomes.
  • Use technology to calculate binomial probabilities, mean or variance and answer cumulative or threshold questions.
  • Check model assumptions and interpret the probability or expected result in context.

Learn this topic

Study SL 4.8—Binomial distribution conceptsOpen the corresponding Concept lesson for explanations, examples and exam connections.

IB Maths AI SL 4.8 Binomial Distribution Questions question 1

[Maximum number: 6]

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 .

Question (a)

(a)

Team X are competing in the tournament. There are 20 athletes in this team. It is known that none of the athletes in Team X use banned substances.

Calculate the probability that none of the athletes in Team X will test positive.

[ 4 ]

Question (b)

(b)

Determine the probability that more than 2 athletes in Team X will test positive.

[ 2 ]
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