Worked solution · Exam P
This Exam P sample reference tests Equally Likely Outcome Counting. Among 36 ordered dice outcomes, 24 have absolute difference zero, one, or two. Thus the probability is 24/36=2/3, choice E.
Independent solution
Setup
The two fair dice produce 36 equally likely ordered outcomes.
Model
An absolute difference below three allows differences zero, one, and two. Count six equal pairs and both orders for each unequal pair.
Compute
The favorable counts are six, ten, and eight for the three allowed differences, totaling 24 of the 36 outcomes.
Answer
The requested dice probability is two thirds.
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Original practice · fully worked
Two fair eight-sided dice, numbered 1 through 8, are rolled independently. Find the probability that the absolute difference between the two results is less than 2.
There are 8 equal pairs and 14 adjacent ordered pairs, so 22 of 64 outcomes qualify. The probability is 11/32, choice D.
Setup
The two eight-sided dice produce 64 equally likely ordered outcomes.
Model
An absolute difference below two permits equal results and adjacent results only. There are eight equal pairs and fourteen ordered adjacent pairs.
Compute
Thus 22 of the 64 outcomes qualify, which reduces to eleven thirty-seconds.
Answer
The probability is eleven thirty-seconds.
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