Lesson Element

Using frequencies in tree diagrams to calculate probabilities

Task 1 Basic probability


There is a 0.02 probability of winning some prize with a National Lottery ticket. If I buy a ticket a week for a year, about how many winning tickets do I expect to get?


A doctor tells your uncle he has a 15% chance of a heart attack in the next 10 years. Out of 100 men like your uncle, how many would you expect to have a heart attack in the next 10 years?


In Dumpsville, in past years it has typically rained on 6 days in June (which has 30 days). Assuming the climate has not changed, if I plan to visit Dumpsville next June, what is the probability the daywill be dry?


Experience has shown out of every 100 racing cyclists, 20 will have been doping. If I pick a cyclist at random, what is the probability that he will be ‘clean’ (not doping)?

Task 2 Comparison of probabilities


If I buy a ticket in Super Lottery, there is a 1% chance of winning something, while a ticket in the Duper Lottery has a 3% chance of winning a prize. If I intend to buy 100 tickets, how many more times will I win if I buy Duper tickets rather than Super tickets?


Typically it rains on 6 days in June (30 days). I am told that in September there is double the chance of raining on any day. What is the chance that it will rain on a random day in September?


It is reported that people who are left-handed are ten times as likely to be left-footed as people who are not left-handed. 92% of those who are right-handed are right footed. What is the chance that someone who is left-handed is right-footed?

Task 3 Conditional probabilities

A fair coin is flipped to decide whether your cricket team is going to bat first or second – heads you bat first, tails you bat second. If you bat first, your team wins 80% of the time. If you bat second, you win 50% of the time.


Out of 100 games, how many do you bat first in?


Out of 100 games, how many do you bat first, and then win?


Out of 100 games, how many do you win?


Before you flip the coin, what is the probability of you winning the game?


100 students are suspected of cheating in an exam. They are wired up to a lie detector that will go ‘ping!’ if it thinks they are lying. The people who make the detector claim that, if you are lying, there is a 90% chance the machine will go ping! If you are genuinely not lying, there is a 10% chance the machine will get it wrong and go ping! Suppose 10 of the students have really been cheating. For how many students will the machine go ping!?

Task 4 Reverse conditional probabilities


Cricket: of the times you win your match, what proportion did you bat first?


Lie detector question – what is the chance, if the machine goes ‘ping!’, that the suspect has been cheating?

June 2015