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IB Maths AI SL 4.8 Binomial Distribution

IB Maths AI SL 4.8 Binomial Distribution
IB Mathematics: applications and interpretation guide, first assessment 2021

Practise checking binomial assumptions, defining X ~ B(n,p) and calculating exact, cumulative or complementary probabilities and expected counts with technology.

How this is tested

  • verify fixed trials, two outcomes, independence and constant p before choosing a binomial model
  • translate exactly, at most and at least into the correct point or cumulative probability
  • use a complement for upper-tail events and interpret the probability or expected count in context

Question 10

[Maximum number: 7]

In a job assessment there are 15 multiple choice questions, each with 5 answers. Only one answer is correct for each question.
Adil completes the assessment by randomly choosing every answer. All answers are equally likely to be chosen. Each of Adil's choices are independent.

Question 10(a)

(a)

Write down the expected number of correct answers.

[ 2 ]

Question 10(b)

(b)

Find the probability that Adil correctly answers exactly 3 questions.

If Adil answers 7 or more questions correctly, he will be offered a job.

[ 3 ]

Question 10(c)

(c)

Find the probability that Adil is offered a job.

[ 2 ]