Can someone look at these 2 questions and explain why in 18) they found the % of survival for 1 class as %survive after 5 years/%survive after 1 year? as the chance of surviving 5 years after 1 year In 20) however they found only the %survive after 5 years and multiplied them together. Shouldn't they divide by % survive after 1 year for both categories then multiply?
You've basically got to look really closely at the content of the question. If I was doing it I would have taken the question and underlined the following:
"If you have had
colon cancer and
have survived for a year, according to the data, what is the chance
that you will survive for 5 years?"
Next thing I would've done is make it simpler by forgetting percentages and looking at it as numbers of people. So say there were 1000 people with colon cancer. 800 survive for one year and 200 do not. 600 survive for 5 years and 400 do not. Those 400 include the 200 that did not survive for one year. Thus out of the 800 that survived for one year, 600 survived for five years and 200 did not. Thus you can say it's a 75% survival chance if you are amonsgt those 800.
"If you
have been diagnosed with lung and breast cancers, according to the statistics, what are the
chances that you will survive for 5 years after treatment?"
Key thing is that time = 0. The person has just been diagnosed. If 1000 people were diagnosed with lung cancer, only 100 of them would survive for 5 years. If 1000 people were diagnosed with breast cancer, 820 of them would survive for 5 years. If one was diagnosed with both, then (although not sure if this is a proper scientific conclusion but I guess you just have to go with it), one could say they had a 10% chance of surviving the lung cancer, and if they were amongst the 100 that managed to survive the lung cancer, there was an 82% chance that they would furthermore survive the breast cancer. That means if there were 1000 people diagnosed with both, around 82 would manage to survive both in 5 years. So that's how they came to the answer of 8.2%
Does that help?