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Need help with question 31

Need help with question 31-example-1
User Carline
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If AC = CD, then each is half of AD, so each has length 12/2 = 6.

If AB = BC, then each is half of AC, so each has length 6/2 = 3.

The lengths are:

... AB = 3

... AC = 6

... AD = 12

... BC = 3

... BD = 9

... CD = 6

Since we have just listed the lengths of "all segments in the diagram," we presume that is the list from which our random segment is chosen. Of these 6 segments listed, 4 are longer than 3. The probability of interest is ...

... 4/6 = 2/3

_____

If you consider the segments in the diagram to be only AB, BC, and CD, then your probability is 1/3, since only CD is longer than 3.

User Canor
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