comparing probabilities

David Green undertook projects in England, exploring student's understanding of probability

these resources are based on one of his tasks

a ppt is here

an intention is to work with student's more 'intuitive' understandings (of ratio) to begin with: e.g doubling amounts in one or other of the jars
and then work towards using common denominator fractions

students can have interesting discussions, occasionally heated, about which jar has a better chance of a 'success'
these notions can be:

• a misconception (same number of ... in each, or, more .... in this one, or, a bigger difference between the two in this one)
• based on good insights about ratio (if you double the number in A...)
• created by an appreciation of unit ratios (there is one ... to one and a half....) 
• an equivalent fraction technique (possibly compared as decimal or percentage equivalents)        

success fractions can be easily compared (with squared paper) by plotting the denominator across and the numerator up and comparing the steepness (gradients) of the lines formed by joining these points to the origin