Year 10 Maths • AC9M10P01 • Authored homework
Conditional probability language
Use the language of “if ... then”, “given”, “of”, “knowing that” and “conditional on” to interpret conditional probability statements and avoid confusing joint, conditional and simple probabilities. Show working, use correct notation and check reasonableness.
Part A
Short-answer questions
What does “given that” mean in probability?
Rewrite “the probability of A given B” using probability notation.
Explain the difference between P(A) and P(A given B).
What does P(A and B) mean?
What does P(A or B) mean?
A card is known to be red. How does this change the sample space?
Explain why conditional probability depends on the information already known.
Give one everyday example of conditional probability language.
What is the meaning of “if a student plays sport, then what is the chance they also play music?”
Correct this misconception: “P(A given B) always equals P(B given A).”
Part B
Long-answer questions
In a class of 30 students, 18 play sport, 12 play music and 8 do both. Find the probability a student plays music given that they play sport.
Using the same class data, find the probability a student plays sport given that they play music. Compare the two answers.
A bag has 5 red, 3 blue and 2 green counters. One counter is known not to be green. Find the probability it is red.
A two-way table shows 40 students, with 22 using the bus and 15 owning a bike, including 9 who do both. Use conditional language to answer one probability question.
Explain how the sample space changes when the word “given” appears in a probability question.
Create a Venn diagram situation and write two different conditional probability questions from it.
A medical test example gives the probability of a positive test given a condition. Explain why this is not the same as the probability of the condition given a positive test.
A student confuses “of the students who passed, how many studied?” with “of the students who studied, how many passed?” Explain the difference.
Write and solve a conditional probability problem using a table, including numerator, denominator and final interpretation.
Compare simple probability, joint probability and conditional probability using one consistent example.
Part C
Research and understanding task
Find or create a two-way table about a real context, such as sport and music, transport and year level, or app use and study time. Write two conditional probability questions and explain why their denominators are different.