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 day will 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?
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 day will 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?
236465-tree-diagrams-lesson-element-student-worksheet.docx