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Table 2 Examples of students’ explanations within the categories, C, MM, AIs

From: Evidence of probability misconception in engineering students—why even an inaccurate explanation is better than no explanation

Tasks Categ. Examples of students’ explanations
Maternity hospital C “Smaller sample implies higher deviation.”
MM “In the first maternity hospital more babies are born, thus there will be more boys and more days.”
AI “I have the chance of 33.3% to get this answer right.”
Lotto C “Each number can be drawn with equal probability, therefore, each combination of seven numbers has the same probability of being drawn.”
MM “Because numbers are in no particular order.”
AI “The lotto is rigged.”
Mobile phones C “The only information we have is the ratio of men and women, and there is no information about their answers. Based only on the provided information, we cannot claim which sex uses the mobile phone more.”
MM “In the first group the number of women exceeds the number of men and the percentage of mobile phone users is higher. In the second group the number of men exceeds the number of women, and the percentage of mobile phone users is lower.”
AI “Because women are more cautious drivers.”
IT engineer C “70% of 100% graduates have that degree.”
MM “Regardless of the number of employees chances of Milan being an engineer and a lawyer are equal.”
AI “intuition”, “it just makes sense to me”
R/W balls C “Numerous attempts are offered, hence the chances are greater.”
MM “It is more probable to draw one ball where the chances are 50-50, than to draw seven consecutive red or white balls.” Or “Because we have 90% of red balls, and because balls are put back into the box after each draw.”
AI “It cannot be known”, “Intuition...”
Lawyer C “Percentage of lawyers is much higher than the percentage of musicians who are members of philharmonics.”
MM “This statement is more probable because he was oriented in this direction in his childhood.”
AI “I believe that both claims are equally probable, but I will opt for an ‘a’.”