EduNinja

IB Maths AA SL 4.8 Binomial Distribution

IB Maths AA SL 4.8 Binomial Distribution
IB Mathematics: analysis and approaches guide, first assessment 2021

Practise recognising binomial conditions, defining X ~ B(n,p) and calculating exact or cumulative probabilities, means and variances with technology or formulae.

How this is tested

  • verify fixed trials, two outcomes, independence and constant probability before using a binomial model
  • define X ~ B(n,p) and distinguish exactly, at most, at least and inclusive probability ranges
  • use np and np(1-p) for mean and variance or solve an unknown binomial parameter

Question 6(a)

[Maximum number: 4]

Two machines are used in a factory to manufacture semiconductors. Machine A manufactures defective semiconductors 10 % of the time, while machine B manufactures defective semiconductors 5 % of the time.
A randomly selected machine manufactures ten semiconductors.
Both machines are equally likely to be selected.

Find the probability that exactly two semiconductors are defective.