4.8 Binomial Distribution

  2. Statistics and Probability
  3. 4.8 Binomial Distribution
    4. 30'
In this chapter we are going to explore probabilities in events where there are only two possible outcomes. This could be success or failure, truth or lies, accuracy or inaccuracy, etc. These particular types of events share characteristics that mean we can calculate probability using the binomial distribution.

Key Concepts

In this unit you should learn to…

  • understand what types of data are binomially distributed

  • be familiar using binomial notation

  • calculate the expected value, standard deviation and variance of a binomially distributed event

  • calculate probability using the binomial distribution

  • calculate probability using the binomial distribution

 

Essentials

1. Introduction

What types of data are binomially distributed? Notation and examples.

 

 

 

 

2. Expected Value, variance and standard deviation

How can we use our knowledge to calculate the expected value, variance and standard deviation of an event?

 

 

 

 

3. Calculating Probability using the binomial distribution

How can we calculate the probability of a particular number of outcomes occurring?

 

3. Calculating Probability using the binomial distribution

How can we calculate the probability of a certain range of numbers of outcomes occurring?

 

Summary

 

 

Test yourself

Self Checking Quiz

Exam Style Questions

The following questions are based on IB exam style questions from past exams. You should print these off (from the document at the top) and try to do these questions under exam conditions. Then you can check your work with the video solution.

Question 1

Ms Roberts teaches a Maths class with 17 students. 6 of them are working from school, and 11 of them are working remotely. 

Each day, Ms Roberts chooses one student at random to make a presentation. 

a. Find the probability that on a given day, Ms Roberts chooses someone who is working from home  (1)

In September, Ms Roberts will teach 15 lessons with her class. 

b. Find the probability that she chooses a student working remotely 8 times.  (2)

c. Find the probability that she chooses a student working in school at least 9 times.  (3)

(6 marks)

Video Solution

 

Question 2

The probability that my train is late on any given day is 0.3. What is the probability that it will be late at least three times between Monday and Friday?  (4)

Video Solution

 

Question 3

An infectious virus is spreading through a school. The probability of a randomly selected student having the virus next week is 0.2. Mr Santos has a class of 24 students. 

a. Calculate the probability that 3 or more students in Mr Santos’ class will have the virus next week.  (3)

b. If more than 25% of the students have the virus next week, the exam will be cancelled. What is the probability that the exam is cancelled?  (4)

(6 marks)

Question 4

A wind turbine has 15 different working components, and works as long as at least of them is working. The probability that an individual component fails in a given year is 0.9. Given that the probability of each individual component failing is independent of the others:

Find the probability that the wind turbine will fail in the first year.  (2)

 

 
 
MY PROGRESS

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